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DEPARTMENT OF — 


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CHAMPAIGN, ILLINOIS. 


Books are Not to be taken from the Library Room. 


Return this book on or before the 
Latest Date stamped below. 


University of Illinois Library 


L161—H41 


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EXPERIMENTAL SCIENCE SERIES FOR BEGINNERS. , 


mie) CRN ale: 


‘SIMPLE, ENTERTAINING, AND INEXPENSIVE) EXPERI 
MENTS ‘IN THE PHENOMENA OF SOUND, 
FOR THE USE OF STUDENTS 
“OF EVERY AGE, 


BY 


ALFRED MARSHALL MAYER, \%3« 


“Professor of Physics in the Stevens Institute of Technology. Member of the 
National Academy of Soiences ; of the American Philosophical Society, 
Philadelphia; of the AmevicanAeg demy of Arts and Sciences, 
Boston; of theNew-¥ 4 CAdEMYO, pdctences ; of the 


German Ast j 0 American 
Q vorgr ber - 
oe dphitainolopledl ‘Sockety, 
[RRARV \ 
AL \ a ae 
nef ys 


NEW YORK: 
an APPLETON AND ocean aa 


549 AND 551 BROADWAY. 
1879. 


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ty ats 
rd 


COPYRIGHT BY 
ALFRED M. MAYER, 
1878. 


I DEDICATE 


THIS BOOK TO MY GOOD FRIEND, 


JOSEPH HENRY. 


WHO INSPIRED MY YOUTH 
WITH A LOVE OF 


THE ART OF EXPERIMENTING, 


i ie a ES ad 


4 


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Lar! A 
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5 CEP er hee et 


PREFACE. 


Tue books of the “Experimental Science Series for 
Beginners” originated in the earnest and honest desire 
to extend a knowledge of the art of experimenting, and 
to create a love of that noble art, which has worked so 
much good in our generation. 

These books, though written for all those who love 
experiments, and wish to know how to make them with 
cheap and simple apparatus, will, it is hoped, be found 
useful to teachers, and especially to the teachers and stu- 
dents in our Normal Schools. The majority of those who 
go from these schools will be called to positions where 
only a small amount of money can be obtained for the 
purchase of the apparatus needed in teaching science. 
These little books will show how many really excellent 
experiments may be made with the outlay of a few dol- 
lars, a little mechanical skill, and—patience. This last 
commodity neither I nor the school can furnish. The 
teacher is called on to supply this, and to give it as his 
share in the work of bringing the teaching of experimen- 
tal science into our schools. 


a laa PREFACE. 


When the teacher has once obtained the mastery over 
the experiments he will never after be willing to teach 
without them ; for, as an honest teacher, he will know 
that he cannot teach without them. 

Well-made experiments, the teacher’s clear and sim- 
ple language describing them, and a free use of the black- 
board, on which are written the facts and laws which the 
experiments show—these make the best text-books for 
beginners in experimental science. 

Teach the pupil to read Nature in the language of ex- 
periment. Instruct him to guide with thoughtfulness the 
work of his hand, and with attention to receive the teach- 
ings of his eyes and ears. Books are well—they are in- 
dispensable in the study of principles, generalizations, and 
mathematical deductions made from laws established by 
experiment—but, “Ce n’est pas assez de savoir les prin- 
cipes, il faut savoir MANIPULER.” 

Youths soon become enamored of work in which 
their own hands cause the various actions of Nature to 
appear before them, and they find a new delight in a 
kind of study in which they receive instruction through 
the doings of their hands instead of through the reading 
of books. | 

The object of this second book of the series is to show 
how to make a connected series of experiments in Sound. 
These experiments are to be made with the cheapest and 
simplest apparatus that the author has been able to devise. 
I have tried to be plain in giving directions for the con- 


PREFACE. ty 


struction and use of this apparatus. In my descriptions 
of the experiments I have endeavored to be clear ; but in 
this I may have failed. If I have, I am sure that the ex- 
periments themselves are true, honest, and of good report, 
and will supply all the shortcomings of language, which, 
even from the best pens, gives but a weak and incomplete 
conception of an experiment. 

In Chapter II. is given an account of the order of the 
experiments. These have’ been carefully selected, and 
arranged so that one leads to the next. Each experiment 
has been made by me over and over again, and the series 
has been performed before me by beginners in the art. I 
therefore know that they will all succeed if my directions 
are perseveringly followed. The experiments are num- 
bered in order up to 130, so that they may be referred to 
from this work, and from the other books of the series. 

Several of the instruments described are new, and 
many of the experiments are so pleasing in their action 
that they may be of interest to my scientific brethren, and 
to those engaged with college classes. I would refer to 
the instruments or experiments described in Experiments 
1, 2, 17, 33, 34, 43 to 59, 61, 65, 66, 67, 68, 69, 70, 73, 74, 
78, 79, 100, 104, 105, 107, 108, 110, 112, 121, 122, 125, 
126, 127. } 

A lively interest has recently been excited in the sub- 
ject of Sound by two of the most remarkable inventions 
of this century : Bell’s Telephone, and the Speaking and 
Singing Phonograph of Mr. Thomas A. Edison. The first 


8 PREFACE. 


named of these inventions will be described in the fourth 
book of the series ; the second I describe, with two ex- 
cellent engravings, at the end of this volume. 

The experiments have been completed for the remain- 
ing books of the series, which will appear in the following 
order (I. “ Light ;” I. “Sound,” already published) : III. 
“Vision, and the Nature of Light ;” IV. “ Electricity 
and Magnetism ;” V. “ Heat ;” VI. “Mechanics ;” VII. 
“Chemistry ;” VIII. “The Art of Experimenting with 
Cheap and Simple Instruments.” 

Mr. Barnard, who was associated with me in writing 
the book on “ Light,” found that his engagements did not 
permit him to continue his work on the series. 

Since the publication of “ Light” I have received the 
request, from various parts of the country, that I should 
make arrangements with some competent instrument- 
maker, who will supply sets of apparatus to go with the 
books of the series. This I have done, and Samuel 
Hawkridge, instrument-maker to the Stevens Institute 
of Technology, Hoboken, New Jersey, will supply the 
sets of apparatus for “ Light ” and “Sound ” at the rates 
given in his price-list at the end of this volume. The 
separate pieces of the apparatus for “Sound” are num- 
bered to correspond to the numbers of the experiments in 
the book. By this plan the purchaser knows which pieces 
of apparatus go together, and is also informed of their 
uses. The student may find it cheaper to hunt up the 
materials, and then make his own apparatus; but so 


PREFACE. 9 


many have desired to have the sets ready for use that I 
have complied with their request. Of course it will be 
understood that the instrument-maker must be paid for 
the time taken in finding the objects in the market, and 
for the labor and skill spent in making the apparatus, 
and in packing it in convenient boxes. 


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CON TENS. 


PREFACE 


CHAPTER I. 
Introduction . 
’ The Construction and tee of the Heliostat 
/The Water-Lantern 


CHAPTER ILI. 


ON THE ORDER OF THE EXPERIMENTS IN THIS Book 


CHAPTER III. 
On THE NaTuRE oF SouND 


CHAPTER IV. 
On THE NaTuRE or Visratory MOTIONS 
The Conical Pendulum 
The Sand-Pendulum . 
An Experiment which gives the Trace of a Vibrating Pine Rod 


PAGE 


24 


27 


The Pendular Motion reproduced from the Traces of the Pendulum 


and of the Vibrating Rod . 
Blackburn’s Double Pendulum 
. Fixing the Curves of Blackburn’s eenaetonl on ihe : 
Experiments in which the Motions of Two Vibrating Rods are made 
_ to trace the Acoustic Curves . 
The Way to draw the Acoustic Curves . 


CHAPTER V. 


On A VisratTine Soup, Liquip, or GasEous Bopy BEING ALWAYS 
THE ORIGIN OF SOUND . 

Experiments with a Tuning-Fork 

Experiments with a Vibrating Tuning-Fork aie a Cork ‘Ball 


12 CONTENTS. 


PAGE 


Experiments with a Brass Disk : : . ‘ 

Experiment in which a Submerged Flageolet is ifemed by forsigg 
Water through it 

Prof. Kundt’s Experiment, made with a Whistle and a Circnt Chimn- 
ney, showing that, as in Wind Instruments, a Vibrating Column 
of Air may originate Sonorous Vibrations 


CHAPTER VI. 


ON THE TRANSMISSION OF SONOROUS VIBRATIONS THROUGH SOLIDS, 
Liquips, AND GASES, LIKE AIR 

Experiment with a Tuning-Fork and Wooden Rod : 

Experiment in which Sonorous Vibrations are sent through Water 

Experiments showing that the Air is constantly vibrating while 
Sonorous Vibrations are passing through it 

Experiments with the Sensitive-Flames of Govi and Barry, aa of 
Geyer 


CHAPTER VII. 


On THE VELOCITY OF TRANSMISSION OF Sonorous VIBRATIONS, AND 
ON THE MANNER. IN WHICH THEY ARE PROPAGATED THROUGH 
Exastic Bopres 

On the Speed with which soneriid Winestete Rees 

Experiments with Glass Balls on a Curved Railway 

Experiments with a Long Brass Spring, showing how viorelacus are 
transmitted and reflected : 

Explanation of the Manner in which Saiseees Vibrations are prop- 
agated 

Experiments with Crova’ s Disk, shorire how Sanvions Vibration: 
travel through Air and other Elastic Matter 


CHAPTER VIII. 


On tHE INTERFERENCE OF Sonorous VIBRATIONS AND ON THE 
Beats or Sounp 

Experiments in Interference of Sound penie with a Trainee ork and 
a Resounding-Bottle 

Experiments in which Interference of Bound is ebieined with a Fork 
and Two Resounding-Bottles 

Experiment showing Reflection of Sound ee a Flat ae Fant 3 


66 


69 


70 


73 
73 
74 
75 


80 


84 
84 
85 
87 
89 


91 


98 


102 


102 
104 


CONTENTS. 13 


PAGE 
Experiments in which, by the Aid of a Paper Cone and a Rubber 
Tube, we find out the Manner in which a Disk vibrates. 105 
Experiments with Beating Sounds . 5 : a . 106 
CHAPTER. IX. 
On THE REFLECTION oF Sound . : . 110 
Prof. Rood’s Experiment, showing the eflestion of Sound ne a 
CHAPTER X. 
On THE Prrcu or Sounps . ae A ale « : 113 
Experiments with the Siren . : : a hie 
Experiment with the Siren, in which is found the amber of Vibra- 
tions made by a Tuning-Fork in one Second F 118 
On finding the Velocity of Sound with a sa Fork and a Rea: 
nant Tube ‘ 120 
On the Relative Numbers we Vabcone per ven d given ns Phan 
Pipes of Different Length . ; ; ‘ P 122 
CHAPTER XI. 
On tne Formation or THE Gamur. : 124 
Experiments with the Siren, showing how the Sounds of the Gamut 


are obtained : ~ : : 4 : 124 


CHAPTER XII. 
EXPERIMENTS WITH THE SONOMETER, GIVING THE SOUNDS OF THE 


GAMUT AND THE HaRMONICS . eked 
Experiments with the Sonometer, giving the Heeachic Sanncé 132 
Prof. Dolbear’s Method of making Melde’s Experiments on Vibrating 

Cords ‘ ; 5 : ‘ : : 135 

CHAPTER XIII. 
ON THE INTENSITIES OF SOUNDS. 137 
Experiment showing that as the Swings ofa eciheting Bout cone 
less the Sound becomes feebler - . : : ; 137 


CHAPTER XIV. 
On Co-VIBRATION. . P é . “ty 439 
Experiments with Two ening. Tarks , ‘ 139 
Experiments on the Co-vibration of Two Wires in the Renagmiee 140 
Experiment of swinging a Heavy Coal-Scuttle by the Feeble Pulls 
of a Fine Cambric Thread j ‘ : ‘ . 144 


14 CONTENTS. 


CHAPTER XV. 


On THE CHANGES IN THE Pitcu oF A. VIBRATING BopDy CAUSED BY ITS 
Mortron . 

Experiment in mich the Pitch of a Whistle} is ehaned By Aare 
it round in a Circle : . . 


CHAPTER XVI. 


ON THE QUALITY OF SOUNDS : A ‘ 
Experiments on the Quality of Sounds . 


CHAPTER XVII. 


ON THE ANALYSIS AND SYNTHESIS OF Sounps 

An Experimental Analysis of the Compound Sounds of a Pato 

Experiments in which we make Compound Sounds of Different 
Qualities by combining Various Simple Sounds : 

How the Ear analyzes a Compound Sound into its Simple Sounds 

An Experiment which shows the Motion of a Molecule of Air, when 
it is acted on by the Combined Vibrations of Six Harmonics . 

Experiments in which Compound Sounds are analyzed by viewing 
in a Rotating Mirror the Vibrations of Kénig’s Manometric 
Flames 

Terquem’s Experiment, which Kendens aihis the Motions of | a Vi- 
brating Disk 


CHAPTER XVIII. 


ON HOW WE SPEAK, AND ON THE TALKING MACHINES or FABER AND 
EpIson 

How we speak 

Experiments in which a Toy Tritt pet dais, and a Spchbing 
Machine is made 

Faber’s Talking Machine 

Edison’s Talking Phonograph 


CHAPTER XIX. 


On Harmony anp Discorp: A SHORT EXPLANATION OF WHY SOME 
NOTES, WHEN SOUNDED TOGETHER, CAUSE AGREEABLE AND OTHERS 
DISAGREEABLE SENSATIONS 


Price-List or Apparatus For “Ligur” anp “Sounp” 


PAGE 


143 


143 


145 
145 


148 


148 


150 
152 


153 


156 


163 


(165 


165 


167 
170 
170 


175 
180 


p>. 
Up 


CHAPTER I. 
Pe ir ks OL EAC 1 T ONs, 


To know how the various sounds of Nature and of 
music are made ; to understand the action of the mechan- 
ical contrivances in our throat and ears, with which we 
speak and hear ; to be able to explain the cause of the 
different tones of musical instruments ; to know why cer- 
tain notes sounded together give harmony, while others 
make discord : such knowledge is certainly valuable, cu-. 
rious, and interesting. You may read about these things, 
but a better way is to study the things themselves, by 
_making experiments, and these experiments will tell you 
better than books about the causes and the nature of 
sounds. 

To make an experiment means to put certain things 
in relation with certain other things, for the purpose of - 
finding out how they act on each other. An experiment 
is, therefore, a finding out. 

It is the aim of this book to show you how to construct 
your own apparatus out of cheap and common things, and 
to aid you in becoming an experimenter. The student 
should, with patience and thoughtfulness, make each ex- 


16 SOUND. 


periment in order, for they have been arranged so that 
one leads naturally to the making and understanding of 
the next. If the first, second, or even third trial does not 
give success, do not be discouraged, for the oldest and 
most gifted experimenters often fail ; yet they have made 
noble discoveries in science by their experiments, because 
they had patience and perseverance, as well as skill and 
knowledge. Do not be disheartened, and you will become 
a skillful experimenter. 

In making an experiment, we may work alone, or we 
may perform the work in the company of our friends, so 
that a large number may see what we do, and assist in 
making the experiment. To exhibit an experiment on a 
large scale, so that all the people in a room may see it, we 
need a magic-lantern. A lantern with a good artificial 
light will cost a great deal of money, but by using the 
water-lantern and heliostat, described in the first book of 
this series, and employing the sun for a light, we can ex- 
hibit many of our experiments in sound, in the most beau: 
tiful manner, before a large company, and at a trifling 
expense. | 

At the same time, the lantern is not essential, and if 
you do not wish to use it you can perform all of the ex- 
periments without its aid. 


THE HELIOSTAT. 


The word “heliostat” is formed of two Greek words— 
helios, the sun, and statos, standing. There is an instru- 
ment so named, because it keeps a reflected beam of 
sunlight constantly pointing in the same direction. In 
“Light,” the first book of this series, we have given a de- 
scription of a simple heliostat ; but, as some of our readers 
may not have that volume, we here give a short descrip- 


INTRODUCTION. 


mmm wenn ne mene sera =- 


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Fra. 1. 


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17 


18 SOUND. 

tion of the manner of making and using that instrument : 
The sun, in his daily apparent path through the sky, 
moves as though he were fixed to the surface of a vast 
globe, which makes a daily revolution around an axis. 
This axis is found by drawing a line from a point near the 
pole-star to the centre of the earth, and then continuing 


S. 


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9/6 6" Movaste Mirror. 
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Fia. 2. 


‘this line beyond the earth till it meets the heavens in a 
spot which can be pointed out only by those who live 
south of the earth’s equator. This line is the axis around 
which the sphere of the heavens appears to revolve once 
inaday. The knowledge of this motion of the sun ena- 
bles us to construct an instrument with a movable mirror 


a 


INTRODUCTION. 19 


which will reflect his beams in one direction from sunrise 
to sunset. 

Figs. 1 and 2 are drawings of the heliostat. The 
scale at the bottom of Fig. 1 gives in inches the size of 
the parts of the lower drawing. -H is a round wooden 
rod, which we call the polar axis of the heliostat, because 
it points toward the pole-star when the instrument is in 
the proper position for use. This axis turns freely in a 
hole in the board A B, and in the block AK. A wooden 
washer MY, which is slid over the axis and is fastened to it, 
rests on the block A, and thus keeps the axis from slip- 
ping down. The end # of the axis has a slot cut in it, 
and a semicircle of wood G', which is screwed to the back 
of a board carrying the mirror J, turns in this slot around 
a carriage-bolt, as shown in the figure. This movable 
mirror is fastened to the board either by strings or by 
elastic bands, which go around the ends of the board and 
mirror. ‘The mirror should be of silvered glass, not of 
common looking-glass. It is, as stated in Fig. 2, 9$ inches 
long and 6 inches wide. 

Since the sun in his daily course through the heavens 
appears to move as though attached to the surface of a 
sphere, which revolves on an axis parallel to the polar axis 
of the heliostat, it follows that, if we tilt the mirror V 
so that the sunbeam which strikes it is reflected down- 
ward in the direction of the polar axis H, then, by simply 
turning this axis with the sun.as he moves in the sky, we 
can keep his rays constantly reflected in that direction. 
The dotted line and arrow going from the mirror V to O 
show the direction of the reflected rays. But this is not 
a convenient direction in which to have the sunbeam, so we 
fix at O another mirror, 6 inches high and 54 inches wide, 
which reflects the beam from O to B, through a hole of 5 


20 SOUND. 


inches diameter cut in the board A B. Brackets, 14 x 12 
inches, with their 12-inch sides screwed to the board A B, 
support a shelf D, which holds the mirror 0. 

Each morning in the year the sun appears on the. hori- 
zon at a different point on the celestial sphere, so that on 
different days we have to give the mirror WV a different 
tilt toward thesun. At the equinoxes, that is, on the 20th 
day of March and September, the rays fall at right an- 
gles to the axis HZ, as shown in Figs. 1 and 2, and the 
mirror in Fig. 1 is placed at the proper tilt for those days. 
In Fig. 2 the tilt of the mirror is also given for the days 
of the summer and winter solstices. 

As we go north, say to Boston, the north star rises to 
a greater height above the horizon, so the axis of our 
heliostat at Boston must stand more upright than at New 
York, and have the position marked “ 42° 22’, Boston.” 
Going south, say to New Orleans, we shall see the pole-star 
shining above the horizon, at a height which is one-fourth 
less than the height it appears at in New York ; therefore, 
at New Orleans, the polar axis of the heliostat is lowered 
into the position marked “29° 58'’, New Orleans.” So 
we see that in different latitudes the axis of our heliostat 
has to be placed at different angles with the horizontal 
line. In order that the instrument may work correctly, 
the angle which it should make with the horizon is the 
same as the latitude of the place. These are the angles 
written before the places named in Fig. 2. These changes 
in the slant of the polar axis for different latitudes need 
like changes in the shape of the block A’; but if one first 
draws the correct line in which the axis goes through the 
board A B, the block # can be formed without trouble. 

ExPERIMENT 1.—To place the heliostat in position for 
use, we raise the sash of a southern window, and secure 


INTRODUCTION. 21 


the board A B between its jambs, with the mirrors out- 
side and the polar axis inside the room. With a shawl or 
blanket closely cover that part of the window above the 
board A B, so as to keep out all light except what comes 
into the room through the hole B. The movable mirror 
is now turned toward the sun, and tilted so that the beam 
from it is reflected by the fixed mirror O into a horizontal 
direction, and at right angles to the board A B. If the 
window faces the south the heliostat will work with entire 
success. If the window does not truly face the south, then 
the board A B should be tilted sideways till it does face 
that direction, and any opening thus made between the 
board A £ and the window-sash may be closed with a 
strip of wood. 
THE WATER-LANTERN. 


Tig. 3 represents a wooden box containing a mirror 
placed inside at an angle of 45°, and supported by wood 
slats fastened to the sides of the box. The side of the box 
opposite the mirror is open. In the top of the box is a 
round hole 5 inches (12.7 centimetres) in diameter. In 
this hole rests a hemispherical glass dish, 53 inches (14 
centimetres) in diameter, made by cutting off the round 
top of a glass shade. At the back of the box is a wooden 
slide carrying a horizontal shelf on its top. This slide has 
a long slot cut in it, and, by means of a bolt and nut fas- 
tened to the back of the box, it can be made fast at any 
required height. This slide is 16 inches (40.6 centimetres) 
long, 5 inches (12.7 centimetres) wide, and # inch (19 mil- 
limetres) thick. The shelf is 7 inches (17.8 centimetres) 
long and 5 inches (12.7 centimetres) wide, and has a hole 
34 inches (8.8 centimetres) in diameter cut in its centre. 
A block of wood is fastened to the back of the box in the 


22 


ai 


Ht 


slot, to serve as a guide in raising and lowering the slide 
which carries the lens. On the hole in the shelf rests a large 


INTRODUCTION. 23 


watch-glass, or shallow dish, about 4 inches (10.1 centi- 
metres) in diameter. A plano-convex lens may be used 
in its place. On each side of the shelf are two upright 
wooden arms, and on screws, which go through them, is — 
swung a looking-glass, 7 inches (17.8 centimetres) long 
and 4 inches (10.1 centimetres) wide. 

ExpPERIMENT 2.—Place this lantern before the helio- 
stat, so that the full beam of light will be reflected from 
the mirror upward through the glass bowl and the watch- 
glass.’ Fill each of these with clear water, and then place 
the swinging mirror at an angle of 45°. Hang up a large 
screen of white cotton cloth, or sheet, in front of the lan- 
tern, and from 15 to 40 feet (4.5 to 12.2 metres) distant. 
On this screen will appear a circle of light projected from 
the lantern. Get a piece of smoked glass, and trace upon 
it some letters, and then lay it on the water-lens. The 
image of the letters will appear on the screen, in white on 
a black ground. If they are not distinct, loosen the nut 
at the back of the box, and move the wooden slide up or 
down till the right focus is obtained. 

This water-lantern may now be used for all the work 
_ performed with ordinary magic-lanterns. Place a sheet 
of clear glass over the large lens, to keep the dust out of 
the water, and then you can lay common lantern-slides on 
this as in a magic-lantern. | 


1 Dr. R. M. Ferguson first used a condensing lens made of a glass 
shade filled with water. See Quarterly Journal of Science, April, 1872. 
Subsequently, Professor Henry Morton made a watch-glass filled with 
water, or other liquid, serve for the projecting lens of the lantern. 


2 


24 SOUND. 


Oe Py AOELA ERY OL 


ON THE ORDER OF THE EXPERIMENTS IN: THIS 
BOOK. 


In Chapter I. are explained the construction and use of 
the heliostat and water-lantern. In Chapter IV. we begin 
by experimenting on the three ways in which a body may 
vibrate. We show that it may swing to and fro like a 
pendulum ; that it may vibrate by shortening and length- 
ening ; and that it may vibrate by twisting and untwist- 
ing itself. Then we study the nature of vibratory motions, 
and find that they are like the motion of a swinging pen- 
-dulum ; and the motion of the pendulum we discover is 
exactly like the apparent motion of a ball looked at in the 
direction of the plane of a circle, in which it revolves with 
a uniform velocity. 

We then, in Chapter V., experiment on those vibra- 
tions whose frequency is so great that they cause sound ; 
and show, in this and the next chapter, that whenever we 
perceive a sound some solid, liquid, or gaseous body is in 
a state of rapid vibration, and that these vibrations go 
from the vibrating body to the ear through a solid, liquid, 
or gas—air being generally the medium which transmits 
the vibrations. These vibrations, acting on the ear, make 
the auditory-nerve fibrils tremble, and thus is caused the 
sensation of sound. 


ORDER OF THE EXPERIMENTS. Q5 


In Chapter VIII. are experiments which show how 
these vibrations are transmitted through solids, liquids, 
and gases, to a distance from the source of the sound. 
The knowledge of how the sonorous vibrations travel 
through the air leads to experiments in which we make 
two sonorous vibrations meet, and, by their mutual action, 
or interference, cause rest in the air and silence to the 
ear. This silence may be continuous, or it may be of short 
duration alternating with sound, and in this case we have 
“beats.” 

Chapter IX. gives Professor Rood’s very striking ex- 
periment showing the reflection of sound. In Experi- 
ment No. 73, of Chapter VIIL, I show how we may read- 
ily obtain reflection of sound from a gas-flame. 

In Chapter X. we give experiments with a siren made 
of card-board, and with it show that the pitch of sounds 
. rises with the frequency of the vibrations causing them. 
With the same siren, in connection with a resonant tube 
tuned to a tuning-fork, we determine the number of vibra- 
tions the fork makes in asecond. With the same tube and 
fork we then measure the velocity of sound in air. With 
the same siren, in Chapter XI., the experimenter finds 
that the notes of the gamut are given by a series of vibra- 
tions whose numbers per second bear to one another cer- 
tain fixed numerical relations. 

In Chapter XII. we experiment with a cheap so- 
nometer, and find the law which connects the length 
of a string with the frequency of its vibrations ; then, 
with this law in our possession, we make the sonometer 
give all the notes of the gamut and the sounds of the har- 
monic series. 

In Chapters XIII, XIV., and XV., are described ex- 
periments showing the cause of the varying intensities of 


26 « SOUND. 


sounds, experiments on the sympathetic vibrations of 
bodies, and on the change made in the pitch of a sounding 
body by moving it. - 

The cause of the different quality of sounds is explained 
in Chapter XVI., and then follow, in Chapter X VIL, ex- 
periments on the analysis of compound sounds, and on the 
formation of compound sounds by sounding together the 
simple sounds which compose them. In this chapter is 
also found an experiment in which is reproduced the mo- 
tion of a molecule of air when it is acted on, at the same 
time, by the vibrations giving the first six harmonics of a 
compound sound ; also, directions for making a very sim- 
ple form of Kénig’s vibrating flame, and a cheap revolving 
mirror in which to view the flame. 

Chapter X VIII. .contains experiments on the voice in 
talking and singing. After explaining how we speak, I 
give experiments on the resonance of the oral cavity, and 
then show how a toy trumpet can be made to speak, and 
a talking machine made out of the trumpet and an orange. 
This chapter concludes with accounts of the talking ma- 
chine of Faber, of Vienna, and of the recently invented 
talking and singing machine of ‘Mr. Edison, which is in- 
deed the acoustic marvel of the century. 

Chapter XIX. concludes the book, and gives a short 
explanation of the causes of harmony and discord. 


NATURE OF SOUND. 27 


CHAPTER III. 
ON THE NATURE OF SOUND. 


SOUND is the sensation peculiar to the ear. This sen- 
sation is caused by rapidly succeeding to-and-fro motions 
of the air which touches the outside surface of the 
drum-skin of the ear. These to-and-fro motions may 
be given to the air by a distant body, like a string of a 
violin. The string moves to and fro, that is, it vibrates. 
These vibrations of the string act on the bridge of the 
violin, which rests on the belly or sounding-board of the 
instrument. The surface of the sounding-board is thus 
set trembling, and these tremors, or vibrations, spread 
through the air in all directions around the instrument, 
somewhat in the manner that water-waves spread around 
the place where a stone has been dropped into a quiet pond. 
These tremors of the air, however, are not sound, but the 
cause of sound. Sound, as we have said, is a sensation ; 
but, as the cause of this sensation is always vibration, we 
call those vibrations which give this sensation sonorous 
vibrations. Thus, if we examine attentively the vibrat- 
ing string of the violin, we shall see that it looks like a 
shadowy spindle, showing that the string swings quickly 
to and fro ; but, on closing the ears, the sensation of sound 
disappears, and there remains to us only the sight of the 
quick to-and-fro motion which, the moment before, caused 
the sound. 


28 SOUND. 


Behind the drum-skin of the ear is a jointed chain of 
three little bones. The one, # of Fig. 4, attached to the 
drum-skin, is called the hammer ,; the next, A, is called 
the anvil ; the third, S, has the exact form of a stirrup, 
and is called the stirrup-bone. This last bone of the chain 
is attached to an oval membrane, which is a little larger 
than the foot of the stirrup. This oval membrane closes 


Fie. 4. 


a hole opening into the cavity forming the inner ear ; a 
cavity tunneled out of the hardest bone of the head, and 
having a very complex form. The oval hole just spoken 
of opens into a globular portion of the cavity, known as 
the vestibule, and from this lead three semicircular ca- 
nals, SC, and also a cavity, C, of such a marked resem- 


NATURE OF SOUND. 29 


blance to a snail’s shell that it is called cochlea, the Latin 
word for that object. The cavity of the inner ear is filled 
with a liquid, in which spread out the delicate fibres of 
the auditory nerve. 

Let us consider how this wonderful little instrument 
acts when sonorous vibrations reach it. Imagine the 
violin-string vibrating 500 times in one second. The 
sounding-board also makes 500 vibrations in a second. 
The air touching the violin is set trembling with 500 
tremors a second, and these tremors speed with a velocity 
of 1,100 feet in a second in all directions through the sur- 
rounding air. ‘They soon reach the drum-skin of the ear. 
The latter, being elastic, moves in and out with the air 
which touches it. Then this membrane, in its turn, 
pushes and pulls the little ear-bones 500 times in a second. 
The last. bone, the little stirrup, finally receives the vibra- 
tions sent from the violin-string, and sends them into the 
fluid of the inner ear, where they shake the fibres of -the 
auditory nerve 500 times in a second. These tremors of 
the nerve—how we know not—so affect the brain that we 
have the sensation which we call sound. The description 
we have just given is not that of a picture created by the 
imagination, but is an account of what really exists, and 
of what can actually be seen by tue aid of the proper 
instruments. 

A body may vibrate more or less frequently in a sec- 
ond ; it may swing over a greater or less space; and it 
may have several minute tremors while it makes its main 
swing. These differences in vibrations make sounds higher 
or lower in pitch, loud or soft, simple or compound. It is 
easy to say all this, but really, to understand it, one must 
make experiments and discover these facts for himself. 


30 SOUND. 


CHAPTER IV. 
ON THE NATURE OF VIBRATORY MOTIONS. 


Tue character of a sound depends on the nature of the 
vibrations which cause it, therefore our first experiments 
will be with vibrations which are so slow that we can 
study the nature of these peculiar motions. These experi- 
ments will be followed by others on vibrations of the same 
kind, only differing in this—that they are so rapid and 
frequent that they cause sounds. A correct knowledge of 
the nature of these motions lies at the foundation of a 
clear understanding of the nature of sound. We hope 
that the student will make these experiments with care, 
and keenly observe them. 

EXPERIMENT 3.—At the toy-shops you can buy for a 
few cents a wooden ball having a piece of elastic rubber 
fastened to it. Take out the elastic and lay it aside, as 
we shall need it in another experiment. Get a piece of fine 
brass wire, about 2 feet (61 centimetres) long, and fasten 
it to the ball. The weight.of the ball should pull the wire 
straight, and, if it does not, a finer wire must be used. 
Hold the end of the wire in the left hand, and with the 
right hand draw the ball to one side. Let it. go, and it 
will swing backward and forward like the pendulum of a 
clock. This kind of movement we call a pendulous or 

transverse vibration. 


NATURE OF VIBRATORY MOTIONS. 31 


EXPERIMENT 4.—Cut out a narrow triangle of paper, 
4 inches (10 centimetres) long, and paste it to the bottom 
of the ball. Twist the wire which supports the ball by 
turning the latter half round, and watch the paper pointer 
as it swings first one way and then the other. Here we 
have another kind of vibration, a motion caused by the 
twisting and untwisting of the wire. Such a motion is 
called a torsional vibration. | 

Exprrimment 5.—Take off the wire and the paper and 
put the elastic on the ball. Hold the end of the elastic in one 
hand, and with the other pull the ball gently downward, 
then let it go. It vibrates up and down in the direction 
of the length of the elastic. Hence we call this kind of 
motion a longitudinal vibration. 

These experiments show us the three kinds of vibra- 
tions, transverse, torsional, and longitudinal. They differ 
in direction, but all have the same manner of moving; for 
the different kinds of vibration, transverse, longitudinal, 
and torsional, go through motions with the same changes in 
velocity as take place in the swings of an ordinary pendu- 
lum. These vibrations all start from a position of momen- 
tary rest. The motion begins slowly, and gets faster and 
faster till the body gains the position it naturally has when 
it is at rest—at this point it has its greatest velocity. 
Passing this point, it goes slower and slower till it again 
comes momentarily to rest, and then begins its backward 
motion, and repeats again the same changes in velocity. 

It is now necessary that the student should gain clear 
ideas of the nature of this pendulous motion. It is the 
cause of sound. It exists throughout all the air in which 
a sound may be perceived, and, by the changes in the num- 
ber, extent of swing, and combinations of these pendular 
motions, all the changes of pitch, of intensity, and of quality 


32 SOUND. 


of sound are produced. Therefore, the knowledge which 
we now desire to give the reader lies at the very founda- 
tion of a correct understanding of the subject of this 
book. 

An experiment is the key to this knowledge. It is the 
experiment with 


THE CONICAL PENDULUM. 


An ordinary pendulum changes its speed during its 
swings right and left exactly as a ball appears to change 
its speed when this ball revolves with a uniform speed in 
a circle, and we look at it along a line of sight which 
is in the plane of the circle. 

ExpPERIMENT 6.—Let one take the ball and wire to 
the farther end of the room, and by a slight circular mo- 
tion of the end of the wire cause the ball to revolve in a 
circle. Soon the ball acquires a uniform speed around the 
circle, and then it forms what is called a conical pendu- 
lum; a kind of pendulum sometimes used in clocks. Now 
stoop down till your eye is on a level with the ball. 
This you will know by the ball appearing to move from 
side to side tm a straight line. Study this motion care- 
fully. It reproduces exactly the motion of an ordinary 
pendulum of the same length as that of the conical pendu- 
lum. From this it follows that the greatest speed reached 
during the swing of an ordinary pendulum just equals the 
uniform speed of the conical pendulum. That the appar- 
ent motion you are observing is really that of an ordinary 
pendulum, you will soon prove for yourself to your entire 
satisfaction; and here let me say that one principle or 
fundamental fact seen in an experiment and patiently re- 
flected on is worth a chapter of verbal descriptions of the 
same experiment. 


NATURE OF VIBRATORY MOTIONS. 30 


Suppose that the ball goes round the circle of Fig. 5 
in two seconds; then, as the circumference is divided into 16 
equal parts, the ball moves from 1 to 2, or from 2 to 3, or 
from 3 to 4, and so on, in one-eighth of a second. But to 
the observer, who looks at this motion in the direction of the 
plane of the paper, the ball appears to go from 1 to 2, from 


is 16 9 8 4% 6; 


Fia. 5. 


2 to 3, from 3 to 4, etc., on a line A B, while it really 
goes from 1 to 2, from 2 to 3, from 3 to 4, ete., in the cir- 
cle, - The ball when at 1 is passing directly across the line 
of sight, and, therefore, appears with its greatest velocity; 
but when it is in the circle at 5 it is going away from the 
observer, and when at 13 it 1s coming toward him, and, 
therefore, although the ball is really moving with its regu- 
lar speed when at 5 and 13, yet it appears when at these 
points momentarily at rest. From a comparison of the 
similarly numbered positions of the ball in the circle and 
on the line A JB, it is evident that the ball appears to go 
from A to B and: from B back to A in the time it takes to 
go from 13, round the whole circle, to 13 again. That is, 
the ball appears to vibrate from A to B in the time of one 
second, in which time it really has gone just half round 


ae SOUND. 


the circle. A comparison of the unequal lengths, 13 to 12, 
12 to 11, 11 to 10, ete., on the line A #B, over which the 
ball goes in equal times, gives the student a clear idea 
of the varying velocity of a swinging pendulum. 


THE SAND-PENDULUM. 
£ Nt 
EO 


E a 
i ITTUVUN NNO UL su | 
| 
i] 


i 


iW 


Tih 


FG. 6. 


Fig. 6 represents an upright frame of wood standing 
on a platform, and supporting a weight that hangs by a 
cord. A A is a flat board about 2 feet (61 centimetres) 
long and 14 inches (35.5 centimetres) wide. .b B are 
two uprights so high that the distance from the under 


NATURE OF VIBRATORY MOTIONS. 35 


side of the cross-beam ( to the platform A A is exactly 
41,1, inches (1 metre and 45 millimetres). The cross-beam 
Cis 18 inches (45.7 centimetres) long. At D is a wooden 
post standing upright on the platform. Get a lead disk, 
or bob, 3,3; inches (8 centimetres) in diameter and 2 inch 
(16 millimetres) thick. In the centre of this is a hole 1 
inch (25 millimetres) in diameter. This disk may easily 
be cast in sand from a wooden pattern. , At the tinner’s 
we may have made a little tin cone 1-3, inch (80 milli- 
metres) wide at top and 24 inches (57 millimetres) deep, 
and drawn to a fine point. Carefully file off the point 
till a hole is made in the tip of the cone of about =; inch 
in diameter. Place the tin cone in the hole in the lead 
disk, and keep it in place by stuffing wax around it. A 
glass funnel, as shown in the figure, may be used instead 
of the tin cone. With an awl drill three small holes 
through the upper edge of the bob at equal distances from 
each other. To mount the pendulum, we need about 9 feet 
(271.5 centimetres) of fine strong cord, like trout-line. 
Take three more pieces of this cord, each 10 inches (25.4 
centimetres) long, and draw one through each of the holes 
in the lead bob and knot it there, and then draw them to- 
gether and knot them evenly together above the bob, as 
shown in the figure. On the cross-bar, at the top of the 
frame, is a wooden peg shaped like the keys used in a 
violin. ‘This is inserted in a hole in the bar—at /’in the 
figure. Having done this, fasten one end of the piece of 
trout-line to the three cords of the bob, and pass the other 
end upward through the hole marked /’, then pass it 
through the hole in the key 7’; turn the key round several 
times; then pass the cord through the hole at G, to the bob, 
and fasten it there to the cords. Then get a small bit of 
copper wire and bend it once round the two cords just 


36 SOUND. 


above the knot, as at 7 in the figure. This wire ring, and 
the upright post at the side of the platform, we do not need 
at present, but they will be used in future experiments 
with this pendulum, 

Tack on the platform A A a strip of wood Z. This 
serves as a guide, along which we can slide the small board 
m, on which is tacked a piece of paper. 

ExPERIMENT 7.—F ill the funnel with sand, and, while 
the pendulum is stationary, steadily slide the board under 
it. The running sand will be laid along ZW, Fig. 7, in 
a straight line. If the board was slid under the sand dur- 
ing exactly two seconds of time, then the length of this 
line may stand for two seconds, and one-half of it may 
stand for one second, and so on. ‘Thus, we see how time 
may be recorded in the length of a line. 

- Brush off the heaps of sand at the ends of the line, and 
bring the left-hand end of the sand-line directly under the 
point of the funnel, when the latter is at rest. Draw the 
lead bob to one side, to a point which is at right angles 


b C 


Fig. 7. 


to the length of the line, and let it go. It swings to and 
fro, and leaves a track of sand, @ 6, which is at right an- 
gles to the line Z UY, Fig. 7. 


NATURE OF VIBRATORY MOTIONS. 37 


Suppose that the pendulum goes from a to }, or from 
6 to a, in one second, and that, while the point of the fun- 
nel is just over L, we slide the board so that, in two sec- 
onds, the end 1 of the line Z M comes under the point 
of the funnel. In this case, the sand will be strewed by 
the pendulum to and fro, while the paper moves under it 
through the distance Z MZ. The result is, that the sand 
appears on the paper in a beautiful curve, Z C NV D MM. 
Half of this curve is on one side of Z MY, the other half 
on the opposite side of this line. 

The experimenter may find it difficult to begin moving 
the paper at the very instant that the mouth of the funnel 
is over Z ; but, after several trials, he will succeed in do- 
ing this. Also, he need not keep the two sand-lines, Z IZ 
and a 6, on paper during these trials; he may as well 
use their traces, made by drawing a sharply-pointed pencil 
through them on to the paper. 

By having a longer board, or by sliding the board 
slowly under the pendulum, a trace with many waves in 
it may be formed, as in Fig. 8. 


Fi¢. 8. 


As the sand-pendulum swung just like an ordinary 
pendulum when it made the wavy lines of Figs. 7 and 8, it 
follows that these lines must be peculiar to the motion of 
a pendulum, and may serve to distinguish it. If so, this 
curve must have some sort of connection with the motion 
of the conical pendulum, described in Experiment 6. 
This is so, and this connection will be found out by an 
attentive study of Fig. 9. 


38 SOUND. 


In this figure we again see a 
wavy curve, under the same circu- 
lar figure which we used in explain- 
ing how the motion of an ordinary 
pendulum may be obtained from 
the motion of a conical pendulum. 
This wavy curve is made directly 
from measures on the circular fig- 
ure, and certainly bears a striking 
resemblance to the wavy trace made 
by the sand-pendulum in Experi- 
ment 7. You will soon see that to 
prove that these two curves are 
precisely the same, is to prove that 
the apparent motion of the conical 
pendulum is exactly like the mo- 
tion of the ordinary pendulum. 

Thé wavy line of Fig. 9 is thus 
formed: The dots on A B, as al- 
ready explained, show the appar- 
ent places of the ball on this line, 
when the ball really is at the points 
correspondingly numbered on the 
circumference of the circle. With- 
out proof, we stated that this ap- 
parent motion on the line A B was 
exactly like the motion of a pen- 
dulum. ‘This we must now prove. 
The straight line Z I is equal to 
the circumference of the circle 
stretched out. It is made thus: We 
take in a pair of dividers the dis- 
tance 1 to 2, or 2 to 3, etc., from the circle, and step this 


e 2 ——@ 
we 
M15 I 


NATURE OF VIBRATORY MOTIONS. 39 


distance off 16 times on the line ZW, hence Z M 
equals the length of the circumference of the circle. In 
time this length stands for two seconds, for the ball in 
Experiment 6 took two seconds to go round the circle. 
This same length, you will also observe, was made in the 
same time as the sand-line Z M/ was made in Experiment 7. 
_In Fig. 9 the length Z WV, of two seconds, is divided into 16 
parts ; hence each of them equals one-eighth of a second, 
just as the same lengths in the circle equal eighths of a 
second. ‘Thus the line L WM of Fig. 9, as far as a record 
of time is concerned, is exactly like the sand-line L M of 
Experiment 7, and the line A B of Fig. 9, in which the 
ball appeared to move, is like the line a 0 of Fig. 7, along 
which the sand-pendulum swung. 

Now take the lengths from 1 to 2,1 to 3,1 to 4, 1 to 5, 
and so on, from the line A B of Fig. 9, and place these 
lengths at right angles to the line Z WW at the points 1, 2, 
3, 4, 5, and so on; by doing so, we actually take the dis- 
tances at which the ball appeared from 1 (its place of 
greatest velocity), and transfer them to Z 17, therefore, 
these distances correspond to the distances from Z WV, 
Fig. 7, to which the sand-pendulum had swung at the end 
of the times marked on LZ @ of Fig. 9. 

Join the ends of all these lines, 2 2’, 3 3’, 4 4’, ete., by 
drawing a curve through them, and we have the wavy 
line of Fig. 9. : 

This curve evidently corresponds to the curve Z O NV 
D M of Fig. 7 made by the sand-pendulum ; and it must 
be evident that, if this curve of Fig. 9 is exactly like the 
curve traced by the sand-pendulum in Experiment 7, it 
follows that the apparent motion of the conical pendulum, 
as seen in the plane in which it revolves, is exactly like 
the real motion of an ordinary pendulum, 


40 SOUND. 


ExPERIMENT 8.—To test this, we make on a piece of 
paper one of the wavy curves exactly as we made the one 
in Fig. 9, and we tack this paper on the board L WM of 
the sand-pendulum, being careful that when the board is 
slid under the stationary pendulum the point of the fun- 
nel goes precisely over the centre line Z M (Fig. 9) of 
the curve. 

Now draw the point of the funnel aside to a distance 
from the line Z M equal to one-half of A B, or, what is the 
same, from 5 to 5’ of Fig. 9. Pour sand in the funnel, and 
let the bob go. At the moment the point of the funnel is 
over Z, slide the board along so that, when the point of 
the funnel comes the third time to the line Z J, it is at 
the end © of this line. This you may not succeed in 
doing at first, but after several trials you will succeed, 
and then you will have an answer from the pendulum as to 
the kind of motion it has, for you will see the sand from 
the swinging pendulum strewed precisely over the curve 
you placed under it. Thus you have conclusively proved 
that the apparent motion of the conical pendulum, along 
the line A S, is exactly like the swinging motion of an 
ordinary pendulum. 

As it is difficult to start the board with a uniform mo- 
tion at the very moment the pendulum is over the line 
LL M, it may be as well to tack a piece of paper on the 
board with no curve drawn on it, and then practise till 
you succeed in sliding the board under the pendulum, 
through the distance Z MV, in exactly the time that it 
takes the pendulum to make two swings. Now, if you 
have been careful to have had the swing of your pendu- 
lum just equal to A #, or from 5 to 5’ on the drawing of 
the curve, you will have made a curve in sand which is 
precisely like the curve you have drawn ; for, if you trace 


NATURE OF VIBRATORY MOTIONS. Al 


the sand-curve on the paper by carefully drawing through 
it the sharp point of a pencil, and then place this trace 
against a windew-pane with the drawing of the curve, 
Fig. 9, directly over it, you will see that one curve lies 
directly over the other throughout all their lengths. 

This curve, which we have made from the circle in 
Fig. 9, and have traced in sand by the pendulum, is called 
the curve of sines, or the sinusoid. It is so called because 
itis formed by stretching the circumference of a circle 
out into a line, and then dividing this line, Z © of Fig. 9, 
into any number of equal parts. From the points of these 
divisions, 1, 2, 3, 4, 5, ete., of Z MW, we erect perpendicu- 
lars, 2 2’, 3 3’, 4 4’, 5 5’, etc., equal to the lines a 2, 
b 3, ¢ 4, d 5, etc., in the circle. These lines in the cir- 
cle are called sines ; so, when we join the ends of these 
lines, erected to the straightened circumference, by a 
curve, we form the curve of sines, or the sinusoid. 

The sinusoid occurs often during the study of natural 
philosophy. We may meet with it again in our book on 
the nature of light, and it certainly will occur in our book 
on heat. 


AN EXPERIMENT WHICH GIVES US THE TRACE OF A 
VIBRATING PINE ROD. 


A in Fig. 10 represents a rod 4 feet (121.9 centi- 
metres) long, 1 inch (25 millimetres) wide, and 4 inch (6 
millimetres) thick, made of clear, well-seasoned pine. 
This is fastened by means of small screws to the 
wooden box # standing on a table. This box may . 
be of any convenient size ; but, as it is to be used for 
another experiment, it may be made about 14 inches (35.5 
centimetres) square and 30 inches (76.2 centimetres) 
high. A shoe-box will answer for the purpose. This 


42 SOUND. 


box is placed on the table, and then filled half full of 
sand, and it thus gives us a firm and solid block against 
which to fasten the rod. The lower edge of the rod is 
placed about 14 inch (88 millimetres) above the table, 


Fre. 10. 


with about 3 feet (91.4 centimetres) projecting beyond 
the box. At the free end is fastened a small camel’s-hair 
pencil, with its tip cut off square, When these things are 
in place, get a narrow piece of board, C, just thick enough 
to touch the tip of the pencil on the rod when the board 
is laid on the table under it. Then tack down a strip of 
wood, D, parallel with the rod, to serve as a guide for the 
board. On the board tack a sheet of white paper. Dip 
a pen in thick black ink, and wet the pencil with it. The 
paper-covered board is now laid under the rod, with the 
pencil just touching it. 

EXPERIMENT 9.—Now draw the end of the rod to 
one side and let it vibrate. The pencil will make a trace 
on the paper which is nearly straight. Make it vibrate 


NATURE OF VIBRATORY MOTIONS. 43 


again, and then slide the paper-covered board steadily and 
quickly to the left, and the pencil will make on the paper 
a sinuous trace. 

Examine attentively this wavy line. It looks very 
much like the curve of sines which the sand-pendulum 
traced for us. If it should be exactly like that curve, 
what would it show? Surely, nothing less than that the 
rod vibrates to and fro with the same kind of motion as has 
a swinging pendulum. ‘To test this supposition make the 
following experiment : 

EXPERIMENT 10.—Obtain a trace of the vibrating pine 
rod in which each flexure in the trace is of the same 
length. ‘This we will only get when we move the paper 
with a uniform velocity under the vibrating rod. Now, 
obtain a trace in sand, on another paper-covered board, 
drawn under the sand-pendulum. This trace must be . 
made by swings of the pendulum which exactly equal the 
breadth of the swings made by the vibrating rod. Draw 
the board under the sand-pendulum with different ve- 
locities, till you succeed in making the waves of the 
sand just as long as those made by the vibrating rod. 
That is to say, the distances from 1 to 2, or from 5 to 6, 
of Fig. 8, must be the same in both traces. Now, with a 
pencil, carefully draw a line through the centre of the 
curve traced in sand. Remove the papers from their 
boards, and place one over the other on a window-pane. 
- After a few adjustments, you will see that one curve lies 
exactly over the other, showing that they are exactly the 
same in form. 

Thus you have yourself found out this very impor- 
tant truth in science: A vibrating rod swings to and 
fro with the same kind of motion as has a swinging 
pendulum, 


44 SOUND. 


THE PENDULAR MOTION REPRODUCED FROM THE TRACES 
OF THE PENDULUM AND VIBRATING ROD. 


We have seen that the pendulum and vibrating rod 
give traces of the curve of sines. We now will show 
how, from this curve, we may get again the pendular mo- 
tions which traced it. 

EXPERIMENT 11.—Get a postal-card and cut in it a 
narrow slit »4; inch (1 millimetre) wide, and slightly 
longer than the sinusoidal trace of the vibrating rod, or 
pendulum. Lay this over the trace, near one end, so that 
you can see a small part of the trace through the slit, as 
is shown in Fig. 11. Move the card over the trace, in the 
direction of the line A B, and you will see the little dot 
swing backward and forward in the slit, and exactly re- 
_ peating the motions of the pendulum or vibrating rod. 


Fig. 11. 


We will hereafter see (Chapter VII. and Experiments 
58 and 110) that the molecules of air, and of other elastic 
bodies, swing to and fro in the line of the direction in 
which sonorous vibrations are traveling through them. 
In the above experiment (11), this direction is represented 
by the direction of the length of the slit ; or, as it is gen- 
erally stated, the sound is moving in the direction of the 
length of the slit. 

ExPERIMENT 12.—Another method of exhibiting this 
matter is to take off the pen and fasten, with wax, a lit- 


NATURE OF VIBRATORY MOTIONS. AD 


tle point of tinsel on the end of the rod, so that it just 
touches a piece of smoked glass laid under it. Vibrate 
the rod and slide the glass under it, and we shall get a sin- 
uous trace on the glass. 

To prepare the smoked glass, lay a piece of gum-cam- 
phor, about the size of a pea, on a brick. Then bend a 
piece of tin into the shape of a funnel, about 2 inches 
high, and cut a number of little notches round the bottom. 
Set fire to the camphor and place the funnel over it, 
and then by moving the glass about in the smoke which 
comes from the funnel it will soon be well blackened. 

In exhibiting this trace in the lantern, so that several 
can see it at once, it is best to keep the card. with the slit 
still and move the glass over it, and then the audience will 
see on the screen a white spot on a dark ground, moving 
with precisely the motion of a pendulum. 


BLACKBURN’S DOUBLE PENDULUM. 


ExpErrmMEntT 13.—Let us return to our sand-pendulum. 
We have examined the vibrations of a single pendulum, 
let us now examine the vibrations of a double pendulum, 
giving two vibrations at once. The little copper ring 7, 
in Fig. 12, on the cord of our pendulum, will slip up and 
down, and by moving it in either direction we can combine 
two pendulums in one. Slide it one-quarter way up the 
cord, and the double cord will be drawn together below 
the ring. Now, if we pull the bob to the right or left, we 
can make it swing from the copper ring just as if this 
point were a new place of support for a new pendulum. 
As it swings, you observe that the two cords above the 
ring are at rest. But the upper pendulum can also be 
made to swing forward and backward, and then we shall 


~ 


46 SOUND. 


have two pendulums combined. Let us try this and see 
what will be the result. 

Just here we shall find it more convenient to use the 
metric measure, as it is much more simple and easy to re- 


S=S 
rT 


INTRII i ii mi 
\ ST I IM a 


| 


| 
iI 
| 
| 
1 
| 
1 


. 


| 
| 
| 
| 
| 


2 


= AA Bx =F = 


member than the common measure of feet and inches. If 
you have no metric measure you had best buy one, or 
make one. Get a wooden rod just 39,31, inches long, and 
divide this length into 100 parts. To assist you in this, 
you may remember that 1 inch is equal to 25,4, milli- 
metres. ‘Ten millimetres make a centimetre, and 100 centi- 
metres make a metre. 


NATURE OF VIBRATORY MOTIONS. 47 


Now slide the ring 7, Fig. 12, up the cords till it is 25 
centimetres from the middle of the thickness of the bob. 
Then make it exactly 100 centimetres from the under side 
of the cross-bar to the middle of the thickness of the bob, 
by turning the violin-key on the top of the apparatus. 

At D, Fig. 12, is a small post. This post is set up 
anywhere on a line drawn from the centre of the plat- 
- form, and making an angle of 45° with a line drawn from 
one upright to the other. Fasten a bit of thread to 
the string on the bob that is nearest to the post, and draw 
the bob toward the post and fasten it there. When the 
bob is perfectly still, fill the funnel with sand, and then 
hold a lighted match under the thread. The thread will 
burn, and the bob will start off on its journey. Now, in 
place of swinging in a straight line, it follows a curve, and 
the sand traces this figure over and over. 


Fire. 13. 


Here we have a most singular result, and we may 
well pause and study it out. You can readily see that we 
have here two pendulums. One-quarter of the pendu- 
lum swings from the copper ring, and, at the same time, 
the whole pendulum swings from the cross-bar. ‘The bob 
cannot move in two directions at the same time, so it 
makes a compromise and follows a new path that is made 
up of the two directions. 

3 


48 SOUND. 


The most important fact that has been discovered in 
relation to the movements of vibrating pendulums is that 
the times of their vibrations vary as the square roots of 
their lengths. ‘The short pendulum below the ring is 25 
centimetres long, or one-quarter of the length of the longer 
pendulum, and, according to this rule, it moves twice as 
fast. The two pendulums swing, one 25 centimetres and 
the other 100 centimetres long, yet one really moves twice 
as fast as the other. While the long pendulum is making 
one vibration the short one makes two. The times of 
their vibrations, therefore, stand as 1 is to 2, or, expressed 
in another way, 1: 2. 

EXPERIMENT 14.—Let us try other proportions and see 
what the double pendulum will trace. Suppose we wish 
one pendulum to make 2 vibrations while the other makes 
3. Still keeping the middle of the bob at 100 centimetres 
from the cross-bar, let us see where the ring must be 
placed. The square of 2 is 4, and the square of 3 is 9. 
Hence the two pendulums of the double pendulum must 


Fia. 14. 


have lengths as4isto9. But the longer pendulum isalways | 
1,000 millimetres. Hence the shorter pendulum will be 
found by the proportion 9: 4: : 1,000 : 444.4 millimetres. 
Therefore we must slide the ring up the cord till it is 
444.4 millimetres above the middle of the thickness of 
the bob. 


NATURE OF VIBRATORY MOTIONS. AR 49 
Mm. Mm. 

2 = 1,000: 250.0........ Octave 
:8 = 1,000; 444.4........ vo ee Fifth. 
:4 = 1,000: 562.5........ : Fourth. 
: 5 = 1,000: 640.0........ : Major Third. 
:6 = 1,000: 694.4....... i ) Minor Third, 

ate as 1.000)8194.6. 5°, aes : Sub-Minor Third. 

BS ee LOOU, = 100.0 ns Bec ae | pipe Second. 
pO 1,000 2790.1)... aa Second. 


50 SOUND. 


Fasten the bob to the post as before, fill it with sand, 
and burn the thread, and the swinging bob will make this 
singular figure (Fig. 14). 

EXPERIMENT 15.—F rom these directions you can go 
on and try all the simple ratios, such as 3: 4, 4:5, 5: 6, 
6:7, 7: 8, and 8:9. In each case raise the two fig- 
ures to their squares, then multiply the smaller num- 
ber by 1,000, and divide the product by the larger num- 
ber ; the quotient will give you the length of the smaller 
pendulum in millimetres. Thus the length for rates of 
vibration, as 8 is to 4, is found as follows: 3 X 3 = 
9,4 xX 4= 16, and 2*1000 —562.5 millimetres. 

The table (Fig. 15) gives, in the first and second col- 
umns, the rates of vibration, and in the third and fourth 
columns the corresponding lengths of the longer and 
shorter pendulums. Opposite these lengths are the fig- 
ures which these double pendulums trace. In the sixth 
column are the names of the musical intervals (see page 
49) formed by two notes, which are made by numbers of 
sonorous vibrations, bearing to each other the ratios given 
in the first and second columns. 


FIXING THE CURVES ON GLASS. 


ExPERIMENT 16.—These interesting figures, traced in 
sand by the double pendulum, may be fixed on glass in a 
permanent form ; and, when framed, will make beautiful 
ornaments for the window or mantel, and will remind you 
that you are becoming an experimenter. Procure squares 
of clear glass about’ six inches on the sides, and buy at 
the painter’s a small quantity of French varnish, or clear 
spirit-varnish. Hold one of these pieces of glass level in 
the left hand by one corner, and, with the right, pour 


NATURE OF VIBRATORY MOTIONS. 51 


some of the varnish upon the glass. Let the varnish 
cover half the glass, and then gently tip the glass from 
side to side till the varnish runs into every corner ; then 
tip it up, and rest one corner in the mouth of the varnish- 
bottle, and rock the glass slowly from side to side. This 
will give a fine, smooth coat of varnish to the glass, and 
we may put it away to dry. When-the varnish is hard, 
lay the glass, varnished side up, on the stand, adjust the 
pendulum to make one of the figures, and then fasten it 
to the post. Burn the thread, and stop the motion of the 
bob as soon as the figure is finished. Brush away any 
extra sand that may lie at the ends of the figure, and 
then take the glass carefully to a hot stove. Have some 
wooden blocks laid on the stove, and rest the glass on 
these. Presently the varnish will begin to melt, and then 
the glass may be lifted and carefully put away to cool, 
taking the utmost care not to disturb the sand. When 
the varnish is hard, the sand which has not stuck is re- 
moved by gently rapping the edge of the plate on the 
table. Then we shall have a permanent figure of the 
curve. To preserve it, lay small pieces of cardboard at 
each corner and narrow strips half-way along the edges, 
and then lay another piece of glass over these, and bind 
the two together with paper on the edges. The plate 
may now be placed on the lantern, and greatly magnified 
images of the curves may be obtained on the screen. 


EXPERIMENTS IN WHICH WE COMBINE THE MOTIONS OF 
TWO VIBRATING RODS. 


We have just seen how the double pendulum combines 
into one movement the motions of two pendulums swing- 
ing at right angles to each other. Our experiments have 


LIBRARY 
UNIVERSITY OF ILLINOIS 


52 — 


also taught us that the numerical relation between the 
numbers of swings of the two pendulums is shown by 
the curved figure produced ; so that, knowing the figure, 
we can tell the relative number of vibrations of each 
pendulum, and, from knowing the latter, we can pre- 


x | 
e 


aa 
———————— 


f es 


dict the curved figure that the double pendulum will 
draw. But our experiments have taught us that a vibrat- 
ing rod moves to and fro with the same kind of motion as 
a swinging pendulum. From this it follows that, if by 
any means we can combine into one motion the separate 


NATURE OF VIBRATORY MOTIONS. 53 


motions of two vibrating rods, we shall make these rods 
describe the curved figures traced by the double pendulum. 

The motions of two vibrating rods may be combined 
into one motion by means of a beam of light, which, fall- 
ing on a mirror fastened to the end of one rod, is reflected 
to a mirror fastened to the end of the other rod, while 
from this second mirror the beam is reflected to a screen. 

It is absolutely necessary for the success of these ex- 
periments that the vibrating rods should be fastened to 
bodies which are heavy and firm, and do not vibrate when 
the rods are set in motion. Boxes A and B of Fig. 16, 
about 14 inches square, half filled with sand, gravel, or 
dry earth, make such supports. The rods Cand D are of 
clear, white pine, 4 feet (121.9 centimetres) long, 1 inch 
(25 millimetres) wide, and 4 inch (6.25 millimetres)-thick. 
On the end of each rod is fastened with wax a silvered 
glass mirror, 1 inch square. The upright rod C is fast- 
ened to the side of the box A by two screws, which go 
through the rod and into the box near the edge of its top. 
Another screw fastens the rod to the box at a distance of 
several inches below the upper screws. 'The free end of 
this rod, above the box, is exactly 30 inches (76.2 centi- 
metres). The length of the horizontal rod D can be 
changed at will, for it is clamped to the side of the box 
B by screws, which go through the ends of the two 
pieces of wood /’ and G. Two nails are driven into the 
box under this rod, and serve to guide it in a horizontal 
direction while we slide it out-or in. <A piece of paper, 1 
inch square, with a hole in its centre of 4 inch in diame- 
ter, is pasted on the mirror of the rod C. 

ExprrimEent 17.—To begin the experiment, we place 
the heliostat in the window. The box A has been made 
of such a height that, when placed before the window, 


54 SOUND. 


the centre of the mirror is opposite the centre of the open- 
ing / in the heliostat. We now loosen the screws in 
the clamps /’ and G, and slide the rod DY under the 
clamps till it projects beyond the box exactly 20;+, inches 
(51.91 centimetres). The boxes A and B are now placed 
in such positions that the light, falling on the 4-inch circle 
on the mirror of the rod C, is reflected to the square- 
inch mirror on the rod D, and thence is reflected to a 
white screen S at the other end of the room, on which it 
appears as a little bright circle. 

In Fig. 16 the bright lines show the light coming from 
the heliostat # to the mirror on the rod C, then going 
to the mirror on the rod D, to be reflected by it to the 
screen 8. | 

Now pull toward you the rod C, and let it go. At 
once the bright circle on the screen is drawn out into a 
vertical line. As the width of the swings of the rod be- 
come less and less, the line becomes shorter and shorter, 
and finally contracts to the little bright circle when the 
rod has ceased to vibrate. Now pull aside the rod D, 
and let it go. The little circle on the screen is now 
drawn out into a horizontal line. 

These two motions of the spot of light are at right 
angles to cach other, and are exactly like the motions 
of the two pendulums of the double pendulum. Hence, 
if both rods should vibrate at the same time, we should 
see the circle of light thrown into one of the familiar 
curved traces of the double pendulum. Let us try the 
experiment. Pull both rods aside, and let them go at 
the same instant. At once the little circle vanishes from 
the screen, and there appears in its place this figure 
(Fig. 17). We at once recognize it as the same figure 
which the double pendulum drew in sand when one of its 


NATURE OF VIBRATORY MOTIONS. 55 


pendulums made two swings while its other pendulum 
made one. ‘Therefore, one of these rods swings twice 
while the other swings once. ; 

It may be that the figure on the screen is not station- 
ary, but appears to twist and untwist itself with a sort of 


Fic. 17. 


revolving motion. If it does so, it will go through curi- 
ous changes. The horns of the above figure will split 
open at their ends, as shown at B in Fig. 18, and, while 
they open more and more, they bend more and more into 
a line with each other, until the figure is like an 8, as at 


Fig. 18. 


C. Then the 8 bends in its middle to the right, as in D, 
while its openings close up more and more, until the fig- 
ure A again appears at /, but with the horns pointing 
to the right instead of to the left. Thus the figure 
changes, becoming smaller and smaller, till it vanishes 
into the circle of light from which it sprang. 


56 SOUND. 


By drawing the rod J in or out, or by loading it, or the 
rod C, with a lump of wax, the figure (17) may be made 
stationary as long as the rods vibrate ; and, when this has 
been done, we know that one of the rods makes one vibra- 
tion while the other makes exactly two ; for the twisting 
and untwisting of the figure are caused by one of the 
rods making slightly more or less than one vibration while 
the other makes two. 

Indeed, so delicate is this method of tuning one vi- — 
brating body with another, that it is used as the most — 
precise one known to bring two tuning-forks to any 
required ratio in their vibrations. Hence these figures 
are sometimes called “the acoustic curves.” In testing 
the forks, they are placed, like the rods, with their 
prongs at right angles, and the light is reflected from 
their polished prongs, as is shown in Fig. 16. Then, 
with a file, some of the metal of one of the forks is re- 
moved, either from the ends or base of its prongs, till 
the figure on the screen remains stationary. 


Fie. 19. 


ExPrERIMENT 18.—The rod D is now unclamped, and 
slid out till 24,3, inches (61.388 centimetres) of its end 
project beyond the edges of the clamps and box. The 
clamps are again screwed tightly against the rod. Now, 
on vibrating the rods together, we have on the screen 


NATURE OF VIBRATORY MOTIONS, 5Y 


the figure corresponding to the ratio 2: 3, given in 
Fig. 19. 

ExpERIMENT 19.—Making the experiment with the free 
length of the rod D, of 253 inches (65.09 centimetres), the 
figure on the screen is like that opposite the ratio 3: 4 
of Fig. 15. 

EXPERIMENT 20.—Giving the rod D 2614 inches (66.7 
centimetres) of free vibrating end, it makes with the rod C 
the figure opposite the ratio 4:5 in Fig. 15, showing that one 
rod makes 4 vibrations in the time that the other makes 5. 

You may not succeed the first time in getting these 
figures from the directions I have given. This is because 
the pine rods which you use may have different elastici- 
ties and weights from those which gave us the lengths we 
have put in this book. But, by drawing out or pushing in 
- the rod D, you will, after the expenditure of a little pa- 
tience, find the lengths of the rod D which give the de- 
sired figures. When found, these lengths should be pre- 
served by drawing a lead-pencil across the rod along the 
outer edge of the clamp J” These marks will serve you 
when you wish to repeat these experiments before your 
friends. A piece of wax will assist you in getting the 
right lengths of the rod D. Stick the piece of wax on 
one of the rods. If the figure on the screen becomes 
more quiet, this shows that this rod which carries the 
wax should be lengthened. If the wax shows that the 
rod C should be lengthened, then we shorten the rod D, 
because the rod C always remains of the same length. 


THE WAY TO DRAW THE ACOUSTIC CURVES. 


By the aid of Fig. 5 we explained how one can plot 
on a line, A B, the distances that a pendulum goes 


58 SOUND. 


through in equal small portions of time, by drawing 
perpendiculars to the line A B from the points of 
equal divisions of the circumference of the circle 
above it. In Fig. 5, if we assume that the pendulum 
goes from A to B in one second, then it goes through 
each of the divisions on the line A B in one-eighth of 
a second. | 

The above mode of getting the distances the pendu- 
lum goes over in successive small portions of time will 
serve us to draw at our leisure all the acoustic curves 
given by Blackburn’s double pendulum, or by the two 
vibrating rods. 

For example, suppose we wish to draw the coe 
which is made when the two pendulums of the double 
pendulum, or the two rods in our last experiment, vibrate _ 
in the ratio of 4 to 5; that is, when one pendulum or 
rod makes 4 vibrations while the other pendulum or rod 
makes 5. 

Draw the circle A C B D, Fig. 20, and inclose it in a 
square. Then draw the two diameters A Band CD paral- 
lel to the sides of the square. Divide the half-circumfer- 
ence A C B into 8—that is, twice 4—equal parts, and 
through the points of these divisions, 1, 2, 3, 4, 5, 6,7, draw 
lines parallel to the diameter C D. Now turn the square 
round so that the diameter C D runs right and left. 
Then divide the half-circumference DA C into 10—that 
is, twice 5—equal parts, and through the points of these 
divisions, a, }, c, d, e, f, g, h, 7, draw lines parallel to the 
diameter A 6. By these operations we have drawn a net- 
work of lines in the square 7 / G H. The spaces on 
the line /’ H, or on any line parallel to it, show how far 
one pendulum or vibrating rod moves in equal times. Let 
us suppose these times eighths of a second. The spaces 


a 


NATURE OF VIBRATORY MOTIONS. 59 


on the line #' F; or on any line parallel to it, show how 
far the other pendulum or rod moves in successive eighths 
of asecond. Now let us begin at the corner 4, and sup- 
pose that the point of the funnel of the double pendulum 
is over this corner. Where will the point of the funnel be 


Fic. 20. 


at the end of the first eighth of asecond? By the motion 
of one pendulum it will have moved from # to J, and by 
the motion of the other pendulum it will have moved 
from # to J. Therefore, at the end of the first eighth of 
a second, the point of the funnel will be where the lines 


60 SOUND. 


drawn through the points J and J meet. For a like rea- 
son, at the end of the second eighth of a second, the pen- 
dulum-bob is at the point of meeting of the two lines 
drawn through the points A and Z. It now at once ap- 
pears how to draw the figure. Begin at the corner Z, 
- and draw a line to the opposite corner of the little paral- 

lelogram J “4 J; then continue the line to the next diag- 
onally opposite corner, always passing diagonally from 
corner to corner of the successive parallelograms. Never 
leave any parallelogram, save at the corner, and you will 
end by tracing the complete figure, and then you will 
find the point of your pencil in the corner 7. 

In like manner, the curves corresponding to any given 
ratio of vibrations may be drawn. ‘The formation of 
these curves is a very fascinating occupation. After you 
have gone over one with a lead-pencil, you may widen the 
line with a drawing-pen, or a camel’s-hair pencil dipped in 
Indian-ink. If you should hang up in your room these evi- 
dences of your progress in the art of experimenting, no 
one will call you vain. 

EXPERIMENT 21.—One more experiment, and we will 
begin the study of vibrations giving sound. 

Draw one of the acoustic curves in a square of 3 inches 
on a side, and place the figure so that its centre is directly 
under the point of the funnel of the double pendulum 
when this is at rest, and see that the sides of the 
Square are parallel to the edges of the base-board of 
the pendulum. 

The double pendulum having been accurately adjusted 
to trace the figure under it, draw the bob aside so that the 
point of its funnel is exactly over the corner of the square 
containing the figure. Pour sand in the funnel, and burn 
the thread. The pendulum starts on its journey, and as it 


NATURE OF VIBRATORY MOTIONS. 61 


goes it really seems guided in its motion by the figure 
under it, for it strews the sand over its lines in the most 
precise manner ; showing again, very neatly, that the mo- 
tion of a pendulum is indeed very accurately reproduced 
by looking at a ball in the plane of the circle around which 
it uniformly revolves. 


62 SOUND. 


CHAPTER V. 


ON A VIBRATING SOLID, LIQUID, OR GASEOUS BODY 
BEING ALWAYS THE ORIGIN OF SOUND. 


Iy this chapter it is shown that the mechanical actions, 
which finally result in giving us the sensation of sound, 
always have their origin in some vibrating body, and 
that this vibrating body may be either solid, liquid, or 
gaseous. 


EXPERIMENTS WITH A TUNING-FORK. 


At the music-dealer’s buy two forks marked “ Philhar- 
monic A.” 'These two forks must be rigorously in tune 
with one another. Buy also another fork marked “ Phil- 
harmonic C.” For the present we only need one of the 
A-forks ; the others will be used in future experiments. 

EXPERIMENT 22.—Get a match, and spreading two of 
your fingers apart rest it upon both. Hold the fork in 
the right hand, and strike the end of one prong squarely 
and smartly on the knee, or on a piece of thick paper 
folded over the edge of the table. Now bring the fork 
up under the match. The instant the match is touched 
it flies into the air as if knocked away by a sudden blow. 

EXPERIMENT 23.—Fill a tumbler brimful of water, 
and, starting the fork once more, hold it over the water so 
that the ends of the prongs touch the surface; imme- 


THE ORIGIN OF SOUND. 63 


diately two tiny showers of spray will fly off on either 
side. This makes a startling experiment when seen mag- 
nified upon the screen (see “ Light,” page 79). A blow 
struck on the match, and the water dashed violently out 
of the glass, show that the tuning-fork is in motion, that 
it vibrates or quivers when it is struck. Strike it once 
more and bring it to the ear, and you hear a clear sound, 
a smooth and pleasant musical note. We conclude that 
the motion must be the cause of the sound, for the sound 
ceases when the fork ceases to quiver. 

EXPERIMENT 24.—Put a small piece of wax against 
the broad face of the end of a prong of the fork, and stick 
against this wax the flat head of a tack. The point of the 
tack should be slightly rounded by a file. Place a piece 
of tin-foil on a napkin or piece of cloth, then vibrate the 
fork and draw the point of the tack quickly along the sur- 
face of the foil. The series of dots now seen on the foil 
show that the prong moved to and from the foil as you 
drew the fork over its surface. 

ExpPERIMENT 25.—Fig. 21 represents a square block of 
wood made by-nailing several pieces of board of the same 
size one upon the other. At one side, near the bottom, is 

the tuning-fork driven into a hole in the block, so that it 
_ will be supported in a horizontal position about $ inch (6 
millimetres) from the table. A slender triangular bit of 
tinsel is fixed with wax on the end of one of the prongs 
to serve as a pen. To make the fork sound in this posi- 
tion we need a hammer or drumstick, made by slipping 
a piece of rubber tubing over astout wire. It is, however, 
always better to vibrate a fork by drawing a violin-bow 
over one of its prongs. 

Get a piece of clean glass 3 inches (7.6 centimetres) 
wide and about 8 inches (20.4 centimetres) long. Smoke 


64 | SOUND. 


this on one side with the apparatus described in Experi- 
ment 12, and then slip it, smoked side up, under the tun- 
ing-fork, lifting the fork so that the tinsel-pen on its end 
will not touch the glass. Next, lay a straight strip of 
wood, A B, Fig. 21, beside the glass and fasten it down 
with brads. This is to serve as a guide in sliding the 
plate under the fork. 


Fig, 21. 


Bend the tinsel-pen down so that it just touches the 
glass. While the fork is vibrating, slide the glass quickly 
along the guide, taking pains to move it at the same speed 
all the time. 

Hold the glass up to the light, and you will see a deli- 
cate wavy line, a sinusoidal trace. We cannot see the 
minute movements of the fork, yet here we have a picture 
of these movements., We see and readily read and un- 
derstand its own handwriting. Placed in the water-lan- 
tern, this trace made by the fork may be exhibited on a 
magnified scale before many persons. ‘To preserve this 
autograph of the fork, flow spirit-varnish over the smoked 
side of the glass, and then the picture may be handled 
without injuring it. 


THE ORIGIN OF SOUND. 65 


You must have observed that the fork gave a clear 
musical sound ; and here we must make a distinction be- 
tween a musical sound and mere noise. <A noise is also 
a sound, but an irregular sound. It also is caused by vi- 
brations, but the vibrations are irregular, now fast, now 
slow, confused and disordered. A musical sound is always 
caused by vibrations, simple or compound, which regularly 
repeat themselves, like those of the tuning-fork which you 
have just examined. For convenience, we will call all 
sounds made by regular vibrations “sounds.” All of our 
experiments will have to do with musical sounds, and will 
finally lead to music itself. 


Y EXPERIMENT WITH A VIBRATING TUNING-FORK AND A 
CORK BALL. 


EXPERIMENT 26,—Fig. 22 represents the fork inclined 

by placing a book under one edge of the block. Cut a 
small ball, about the size of a pea, out of cork, and dip it 
in spirit-varnish ; when dry, fasten it to a fibre of fine floss 
silk. Take the end of the fibre in the left hand so that 
the ball will hang free, and then with the hammer in the 
right hand strike the fork a smart blow. At once bring 
the ball to rest against the foot of the prong, just above 
where it joins the handle. Here the ball rests quiet 
against the fork. Now slowly raise the ball, keeping it 
close to the fork. Immediately it. begins to tremble. 
Raise it higher, and it darts away in little jerks and 
jumps. Lift it higher, and it becomes still more agitated, 
and near the end of the fork it is dashed violently away, as 
shown in Fig. 22; it falls back and is dashed away again. 
Now take the fork out of the block, and bring the end 

of its handle against the cork ball. The ball trembles. 


66 SOUND. 


These experiments show that there are places of rest above 
the crotch of the fork, and that the prongs swing to and 
fro about these places of rest, while the handle, or foot of 


Fig. 22. 


the fork, vibrates up and down. Experiment 60 will teach 
us yet more as to the manner in which the prongs vibrate. 
In the above experiments, a small bead, hung by the silk 
fibre, sometimes works as well as the cork ball. 


EXPERIMENTS WITH A BRASS DISK. 


At the hardware-store you can buy a piece of sheet- 
brass 4 inch (8 millimetres) thick and 6 inches (15 cen- 
timetres) square. ‘Take care to get a flat piece, and, if it 
is not perfectly flat, have it hammered out flat at the 
brass-worker’s. Then let the brass-worker cut it into a 


THE ORIGIN OF SOUND. 67 


circle. Let him round off the edges, and cut a hole just 
33; inch (5 millimetres) in diameter in its centre. If the 
brass disk has been hammered, put it in a stove till it is 
red hot, and then take it out and lay it away where it 
will cool slowly. Cut about 6 inches (15.2 centimetres) 
from a rake or broom handle, and set it upright and firm 
in a heavy block of wood. With a knife pare off the 
sharp edges at the top of this upright, and then fit 
a screw tightly to the hole in the brass disk, and 
screw the disk to the top of the upright. We have 
now a flat disk of brass resting firmly on a stout upright 
support. 

EXPERIMENT 27.—Draw a violin-bow carefully over the 
edge of the disk, and after a little practice you will be able 
to make the disk give a clear, strong sound. The bow, 
alternately catching and slipping on the edge of the disk, 
causes it to vibrate, and the vibrations result in sound. 
To make these vibrations visible, get some of the sand we 
used in the sand-pendulum, and scatter it thinly over the 
disk. Now, when the violin-bow causes the disk to vi- 
brate, the sand will be agitated. Each grain will spring 
up and down with a curious, dancing motion. This move- 
ment of the sand shows that the disk is violently agitated ; 
is beating up and down, and tossing the sand about at 
every vibration. 

EXPERIMENT 28.—Touch one finger on the edge of 
the disk, and draw the bow at a point one-eighth of the 
way round the disk, measuring from the finger. We now 
get a most singular result. The sand dances furiously 
about, as before, and immediately gathers in lines, which 
are two diameters at right angles, and one of the diam- 
eters starts from the point where the finger touches the 
disk, as is shown in A of Fig. 28. 


68 SOUND. 


EXPERIMENT 29.—Draw the bow at a point 30° dis- 
tant from where the finger touches the disk, and 6 lines 
of sand will be formed, as at B in Fig. 23. 

EXPERIMENT 30.—By a little practice, a place still 
nearer the finger may be found, where the bow will make 
8 lines of sand, as at Cin Fig. 23. 


Fig. 23. 


To understand these experiments, you will observe 
that, when the bow throws the disk into vibration, the 
sand on its surface is driven about in a kind of tiny waltz. 
Where the finger touches the disk the trembling of the 
disk is nearly stopped, and where the disk is bowed the 
swings of the plate are the greatest ; hence the disk is 
forced to break up into vibrating sectors, each sector be- 
ing twice the width of the distance of the finger from the 
bow. While any one sector is swinging up the adjoining 
sectors are swinging down, and vice versa. If this be so, 
then the disk must always break up into an even number 
of sectors. It always does so. That the disk really vi- 
brates as we have stated, you will conclusively prove for 
yourself by Experiments 68, 69, '70, and 122. 

The lines separating the different sectors remain near- 
ly at rest, exactly like the places just above the crotch of 
the tuning-fork, found out in Experiment 26. ‘The sand, 
dashed about on the vibrating parts, is driven to these 


THE ORIGIN OF SOUND. 69 


places of rest, and gathers in narrow windrows running 
from the centre of the disk. These lines of rest are called 
nodal lines. 

EXPERIMENT 31.—To increase the interest in these ex- 
periments, mix some dry lycopodium powder (from the 
druggist’s) with the sand, and strew the mixture on the disk. 
These powders will behave in the most extraordinary man- 
ner when the disk vibrates, forming little heaps and whirl- 
winds that seem to smoke and boil furiously. This singular 
phenomenon is caused by the rotating currents of air set 
in motion by the vibrating disk. The heavy sand dashes 
through these little whirlwinds, but the light powder is 
caught up and whirled about in strange fantastic dances. 


EXPERIMENT IN WHICH A SUBMERGED FLAGEOLET IS 
SOUNDED BY FORCING WATER THROUGH IT. 


~ EXPERIMENT 32.—Fig. 24 represents a glass jar (a 
bucket will do as well) standing in a sink near a water- 
faucet. A tin flageolet, such as may be bought in the 
toy-shops, has the highest finger-hole in it closed with 
wax, as shown in Fig. 24. All the other holes are left 
open. <A rubber tube leading from the faucet is slipped 
_ over the mouth of the flute. The water is turned on, and 
flows through the tube into the flute, and thence out into 
the jar. The jar overflows, and the water runs away 
down the sides. These things, placed in this manner, 
will give an experiment showing that a liquid, like water, 
-may vibrate and give a sound. If the flow of the 
water is carefully regulated, and the flute is of the right 
pattern, you will hear a low but distinct musical note 
from the water. Touch the glass jar and a piece of pa- 
per laid on the surface of the water, and you will feel 
them quivering with the vibrations. Here we have a flute 


70 SOUND. 


blown by water under water, and giving a sound which is 
caused solely by the vibrations of the water. A queer 


Fie. 24. 


flute, certainly, and an experiment as surprising in its 
effects as it is instructive. 


PROFESSOR KUNDT’S EXPERIMENT, MADE WITH A WHISTLE 
AND A LAMP CHIMNEY, SHOWING THAT, AS IN WIND IN- 
STRUMENTS, A VIBRATING COLUMN OF AIR MAY ORIG- 
INATE SONOROUS VIBRATIONS. 


EXPERIMENT 33.—The chimneys of student-lamps 
have a fashion of breaking just at the thin, narrow part 


THE ORIGIN OF SOUND. V1 


near the bottom. Such a broken chimney is very useful 
in our experiments. At A, in Fig. 25, is such a broken 
chimney, closed at the broken end with wax. <A cork is 
fitted to the other end of the chimney, and has a hole 
bored through its centre. In this hole is inserted part of 
a common wooden whistle. At J is an exact representa- 


Fra. 25. 


tion of such a whistle, and the cross-line at C shows 
where it is to be cut in two. Only the upper part is used, 
and this is tightly fitted into the cork. 

Inside the tube is a small quantity of very fine precip- 
itated silica, probably the lightest powder known. Some 
of this powder you may purchase of Mr. Hawkridge, of 
Hoboken, New Jersey. Hold the tube in a horizontal posi- 
tion and blow the whistle. The silica powder springs up 
into groups of thin vertical plates, separated by spots of 
powder at rest, as in the figure. This is a very beautiful 
and striking experiment. 

EXPERIMENT 33 a.—The following erent shows 
that the sound is caused by the vibrations of the column 
of air in the tube and whistle, and not by the vibrations 
of these solid bodies. Grasp the tube and whistle tightly 
in the hands. These bodies are thus prevented from vi- 
brating, yet the sound remains the same. 

aa 


7p) SOUND. 


The breath driven through the mouth of the whistle 
strikes on the sharp edge of the opening at the side of the 
whistle, and sets up a flutter or vibration of air. The air 
within the glass tube now takes part in the vibrations, 
the light silica powder vibrates with it, and makes the 
vibrations visible. 

To exhibit this experiment before a number of people, 
lay the tube carefully on the water-lantern before the heli- 
ostat, and throw a projection of the tube and the powder 
on the screen. When the whistle is sounded, all in the 
room can see the fine powder leaping up in the tube into 
thin, upright plates. 

EXPERIMENT 34.—Mr. Geyer has made the following 
pleasing modification of this experiment: Take a glass 
tube about 2 feet (61 centimetres) long and ? inch (19 
millimetres) diameter. One end of this tube is stopped 
with acork ; then some silica is poured into it.. The other 
end is placed in the mouth. Singing into the tube, a note 
is soon struck which causes the silica to raise itself in 
groups of vertical plates, separated by places where the 
powder is at rest, the number.of these groups and their 
positions in the tube changing with the note sung. 

We have now seen how solids, like steel or brass, may 
vibrate and give a sound. We have heard a musical 
sound from vibrating water, and these last experiments 
prove that a gas, like air, may also vibrate and give a 
sound. In the next chapter you will find experiments 
which show how these vibrations move through solids, 
through liquids, and through the air. 


TRANSMISSION OF SONOROUS VIBRATIONS. 3 


CHAPTER VI. 


ON THE TRANSMISSION OF SONOROUS VIBRATIONS 
THROUGH SOLIDS, LIQUIDS, AND GASES, LIKE AIR. 


\/ EXPERIMENT WITH A TUNING-FORK AND WOODEN ROD. 


In this chapter it is shown that a solid, a liquid, or a 
gas, like air, may conduct to a distant point the vibrations 
made at the place of origin of the sound. 

EXPERIMENT 35.—Get the tuning-fork and one of the 
pine rods we used in Experiments 9 and 17. Let one hold 
the rod horizontally and lightly pressed against the panel 
of adoor. Let another make the fork vibrate, and then 
press the end of its handle against the free end of the 
rod. At once the door-panel gives the note of the fork. 
Take the fork away from the end of the rod and the 
sound is no longer heard. Why the panel gives so loud a 
sound will be explained by other experiments. Just now 
we are merely observing the fact that the vibrations of 
the fork move through the rod to the door. 

EXPERIMENT 36.—Hold the rod to the ear, and touch 
the fork to the other end, and the sound will be heard 
distinctly. 

EXPERIMENT 37.—If you hold the rod in the teeth 
and clese the ears the sound will be heard, showing that 
the vibrations of the fork travel through the rod, through 
the teeth, and through the bones of the head to the ear. 


"A SOUND. 


EXPERIMENT 38.—Touch the handle of the vibrating 
fork to the head and you will perceive the sound. 

EXPERIMENT 39.—Open the mouth and place in it your 
watch, taking care that your teeth do not touch it, and take 
note of the force of the sound you hear. Now gently bite 
the watch, and note how distinctly the ticks are heard. 

ExpEertMentT 40.—At the toy-shops you can buy a lit- 
tle instrument sometimes called the “lovers’ telegraph,” 
or “telephone.” It consists of two short pieces of tin tube, 
each having a membrane fastened over one end, and a long 
piece of twine joining the two membranes. Let one boy 
hold the open end of one of the tins to his ear, and let 
another take the other tin to the distance at which the 
twine is pulled out tight. ‘Then let him sound the fork and 
touch its foot to the tin ; immediately the boy at the other 
end hears the note. The vibrations of the fork travel 
through the first tin and membrane, then along the twine 
to the other membrane and tin to the ear of the listener. 


AN EXPERIMENT IN WHICH SONOROUS VIBRATIONS ARE 
SENT THROUGH WATER. 


ExPERIMENT 41.—At the carpenter’s procure two 
wooden boxes, measuring on the outside 7? inches (19.7 
centimetres) long, 3 inches (9.84 centimetres) wide, and 
24 inches (6.4 centimetres) deep, using pine } inch (6 mil- 
limetres) thick. In making these boxes, neither dovetail- 
ing nor nails need be used ; they may be glued together. 
One end of the box is left open. Make the tuning-fork 
sound, and then hold it upright, resting the handle on the 
centre of the top of the box. You observe the sound is 
now very much louder. Why this is so will be shown by 
other experiments. 


TRANSMISSION OF SONOROUS VIBRATIONS. %5 


EXPERIMENT 42.—In Fig. 26 is the box. A tumbler 
filled with water is standing on the box. The tuning-fork 
stuck in a block of wood rests on the water. Take the 
fork and block in the hand, and make the fork vibrate ; 
then immediately plunge the block in the water as repre- 
sented in the figure. At once you will hear the sound of 


Fic. 26. 


the fork apparently coming out of the box. The vibra- 
tions of the fork pass through its handle to the block, and 
from this through the water and through the bottom of 
the glass to the box. Our experiment thus shows that 
vibrations may easily pass through a liquid. A sheep’s 
bladder filled with water may replace the tumbler and 
water in this experiment. 


EXPERIMENTS SHOWING THAT THE AIR IS CONSTANTLY 
VIBRATING WHILE SONOROUS VIBRATIONS ARE PASSING 
THROUGH IT. 


We must now add to our apparatus an open metai A- 
pipe, about 74 inches (19 centimetres) long, shown at 


76 SOUND. 


Cin Fig. 27. This pipe the organ-builder will accurately 
tune to your “ A-philharmonic” fork. 

ExPERIMENT 43.—Get a glass tumbler about 23 inches 
in diameter and about 34 inches deep, though any tumbler 
will do. Take a piece of window-glass about 3 inches 
square and place it over the tumbler. The glass must 
touch the edge of the mouth of the tumbler all around. 


Fie. 27. 


Now slowly slide the glass so that the opening into the 
tumbler gets larger and larger, while the vibrating fork is 
held all the time over this opening, as shown at A in Fig. 
27. Presently you will get an opening of a size that 
causes an intense sound, much louder than any you 
have ever before heard from the fork alone. This is 
because the air in the tumbler is set in vibration, and 
adds the vibrations of its mass to those of the fork. That 


> i. 


TRANSMISSION OF SONOROUS VIBRATIONS. VE 


this is so you may prove for yourself by the following 
experiment : 

Exprrmment 44,—Being careful not to move the glass 
plate from its present position (Experiment 43), stick it 
with wax to the tumbler. Pour a little silica into the 
tumbler, and then hold it horizontally, and vibrate the 
fork near its opening, observing attentively how the silica 
powder is acted on by the inclosed vibrating air. 

EXPERIMENT 45.—Take a piece of thin linen paper 
about 44 inches square, and having wetted it paste it over 
the mouth of the tumbler. When the paper_has dried it 
will be stretched tightly...Take a sharp penknife and 
carefully cut away the paper so as to make an opening as 
shown at B in Fig. 27. Make this opening small at first, 
and very gradually make it larger and larger. Hold the 
fork over the opening after each increase in its size, and 
you will soon discover the size of the opening which 
causes the air inclosed in the tumbler to vibrate with the 
fork, and thus greatly to strengthen its sound. You have 
now a mass of air in tune with the fork, and inclosed in a 
vessel which has one of its walls formed of a piece of 
elastic paper. With this instrument, which I have invented 
for you, you must make some charming experiments. 

Exrrrtment 46.—If the air in the tumbler vibrates to 
the A-fork, it will, of course, vibrate to the A-pipe, which 
gives the same note as the fork. Scatter some sand on 
the paper, and then sound the A-pipe a foot or two from 
it. The sand dances vigorously about, and ends by 
arranging itself in a nodal line parallel to the edges of 
the paper, in the form of a U with its two horns united 
by a straight line. The vibrations of the pipe can only 
reach the tumbler by going through the air, and, as the 
sand vibrates when the tumbler is placed in any position 


"8 SOUND 


about the pipe, it follows that the air all around the pipe 
vibrates while the pipe is sounding. 

ExpERIMENT 47.—Sprinkle a small quantity of sand 
on the paper, and then, placing a thin book under the tum- 
bler, so incline it that the sand just does not run down the 
paper, as shown in B, Fig. 27. Now go to the farthest 
end of the room and blow the pipe in gentle toots, each 
about one second long. At each toot, your friend, stand- 
ing near the tumbler, will see the sand make a short march 
down the paper; and soon by a series of marches it makes 
its way to the edge of the paper and falls into the tum- 
bler. I have, in a large room, gone to the distance of 
60 feet (18.28 metres), and the experiment worked as I have 
just described it. 

ExPERIMENT 48.—Again arrange the experiment as in 
Experiment 47, and standing 3 or 4 feet from the tumbler 
try how feeble a sound will vibrate the paper. If every 
part of the experiment is in good adjustment, you will find 
that the feeblest toot you can make will set the sand 
marching. To keep it at rest you must keep silent. 

ExpPERIMENT 49.—To show these experiments on a 
greatly magnified scale, place the tumbler in front of the 
heliostat (sce “Light,” page 79) so that the sun’s rays just 
graze along the inclined surface of the paper. Cut off a 
piece of a match 4 inch long, and split this little bit mto 
four parts. Place one of these on the inclined paper. Of 
course, the image of the tumbler is inverted, so the bit of 
wood appears to adhere to the lower side of the paper. 
If a little paper mouse cut out of smooth paper is used in 
place of the bit of wood, it is really amusing to see the 
mouse make a start to every toot of the pipe. I trust 
my reader will not think me unscientific for making a 
little fun. Singing the note A, instead of sounding it 


TRANSMISSION OF SONOROUS VIBRATIONS. 19% 


on the pipe, produces the same effects in the above ex- 
periments. 

EXPERIMENT 50.—If you sing or sound some other 

note than the A, you will find it powerless to move the 

sand over the tumbler. 

EXPERIMENT 51.—The experiments just made with the 
tumbler, partly covered with the glass plate or stretched 
paper, may be modified in a way that makes one of the 
most beautiful and instructive experiments. 

Take a pint bottle half filled with distilled or rain 
water, and put into it one ounce of shavings of white cas- 
tile soap ; then shake the bottle. If the soap does not all 
dissolve, add more water till you have a clear solution. 
_ Then add a gill of glycerine, shake, and allow to settle. 
This solution is the best for making soap-bubbles. 

Pour out the soap-solution into a basin; then dip the 
mouth of a deep tumbler (one 5 or 6 inches deep is the best) 
into it. The glass plate is now slid through the soap- 
water under the mouth of the tumbler. Take the tum- 
bler, with the glass on it, out of the basin and stand it 
erect on the table. Vibrate the A-fork, and hold it over 
the edge of the tumbler while you slide the glass plate 

across its mouth, as we did in our other experiments. 
‘The opening which is thus made, between the rim of the 
tumbler and the edge of the glass plate, will have a soap- - 
film over it. Adjust the size of this opening till it tunes 
the air in the tumbler to vibrate to the fork. When this 
takes place, a loud sound issues from the tumbler, and the 
delicate soap-bubble is violently agitated ; its surface is 
chased and crinkled in so complicated a manner that its 
appearance cannot be described. 

This experiment succeeds best with a very deep tum- 
bler, like the one we have used, and with a C-fork and 


80 SOUND. 


pipe. The soap-film covers nearly half of the mouth of 
the tumbler when the latter is in tune to the O-fork. 

To see well the vibrating surface of soap-film, you 
must reflect from it the light of the sky. 

EXPERIMENT 52.—By the aid of the heliostat and a 
lens the experiment may be made one of. great beauty. 
With some wax stick the glass plate to the tumbler, so 
that the soap-film may be placed upright and inclined to 
the beam of light coming from the heliostat. With a plano- 
convex lens placed between the film and the screen obtain 
a magnified image of the soap-film (see “ Light,” page 79). 

As the soap-film is upright it drains thinner and thin- 
ner, While the image of the film grows more and more 
brilliant. Magnificent bands of reddish and bluish light 
appear, and stretch across the screen. Now sound the 
fork or pipe near the film. The vibrations bend and un- 
dulate the colored bands, and the colors chase each other 
over the screen like waves on a troubled sea. On the 
sound ceasing, the bands straighten, and a comparative 
calm spreads over the screen. 


EXPERIMENTS WITH THE SENSITIVE-FLAMES OF GOVI 
AND BARRY, AND OF GEYER. 


EXPERIMENT 53.—In Fig. 28, A is an upright wooden 
rod nailed to a block D. At B is a piece of stout wire 
bent in the form of a ring, 5 inches (12.7 centimetres) in 
diameter, and then bent at a right angle and stuck in the 
upright rod. On the ring is laid a piece of wire gauze 
that has about 30 meshes to the inch. /# is a glass tube 
joined to a rubber tube that leads to the nearest gas- 
burner. To make this glass tube or jet, take a piece of 
glass tube, about + inch outside diameter and: 6 inches 


TRANSMISSION OF SONOROUS VIBRATIONS. 81 


(15.2 centimetres) long, and, holding its ends in the hands, 
heat the tube, at about 14 inch from its end, in a spirit- 
flame or the flame of a Bunsen burner till it softens ; 
then pull it out till it is reduced about one-quarter in di- 
ameter. When it is cold, draw the edge of a file across 
this narrow part, and snap the tube asunder. Now heat 
in like manner the middle of this tube, and bend it into a 


right angle, as shown in Fig. 28, and, with wax, stick it 
upright on a block of wood, with the tip of the jet about 
2 inches (5.1 centimetres) below the wire gauze. 

Turn on the gas and light it above the gauze, where 
it will burn in a slender, conical flame, about 4 inches 
high, with its top yellow and its base blue. This forms 
the “sensitive-flame” invented by Prof. Govi of Turin, 
and afterward by Mr. Barry of Ireland. 


82 SOUND. 


If you hiss, whistle, shake a bunch of keys, or clap 
the hands, the flame at once roars, and, shrinking down 
to the gauze, becomes entirely blue and almost invisible. 
It is called a ‘“ sensitive-flame,” because it is sensitive 
to sonorous vibrations, and shows us their existence in 
the air. 

Exprrtment 54,—Mr. Geyer, of the Stevens Institute 
of Technology, has made an addition to the Govi-Barry 
flame, which heightens its sensitiveness, and makes it 
utter a musical note while disturbed by vibrations ; 
while, in another modification of the experiment, the 
flame sings continuously, except when agitated by exter- 
nal sounds. I give his experiments in his own words : 


‘“‘ To produce them it is only necessary to cover Barry’s flame 
with a moderately large tube [see Fig. 28, in which, however, the 
tube is represented of somewhat too great a diameter], resting it 
loosely on the gauze. A luminous flame, 6 or 8 inches long, is 
thus obtained, which is very sensitive to high and sharp sounds. 
If, now, the gauze and tube be raised, the flame gradually shortens, 
and appears less luminous, until at last it becomes violently agi- 
tated, and sings with a loud, untform tone, which may be main- 
tained for any length of time. Under these conditions, external 
sounds have no effect upon it. The sensitive musical flame is 
produced by lowering the gauze until the singing just ceases. It 
is in this position that the flame is most remarkable. At the 
slightest sharp sound, it instantly sings, continuing to do so as 
long as the disturbing cause exists, but stopping at once with it. 
So quick are the responses that, by rapping the time of a tune, 
or whistling or playing it, provided the tones are high enough, 
the flame faithfully sounds at every note. By slightly raising or 
lowering the jet, the flame can be made more or less sensitive, so 
that a hiss in any part of the room, the rattling of keys even in 
the pocket, turning on the water at the hydrant, folding up a 
piece of paper, or even moving the hand over the table, will excite 


TRANSMISSION OF SONOROUS VIBRATIONS. 83 


the sound. On pronouncing the word ‘sensitive,’ it sings twice; 
and, in general, it will interrupt the speaker at almost every ‘s,’ 
or other hissing sound. 

‘‘The tube chiefly determines the pitch of the note, shorter or 
longer ones producing, of course, higher or lower tones respec- 
tively. I have most frequently used either a glass tube, 12 inches 
long and 1} inch in diameter, or a brass one of the same dimen- 
sions. Out of several rough pieces of gas-pipe, no one failed to 
give a more or less agreeable sound. Among these gas-pipes was 
one as short as 7 inches, with a diameter of 1 inch; while an- 
other was 2 feet long and 14 inch in diameter.:: A third gas-pipe, 
15 inches long and # inch in diameter, gave, when set for a con- 
tinuous sound, quite a low and mellow tone. 

“If the jet be moved slightly aside, so that the flame just 
grazes the side of the tube, a note somewhat lower than the fun- 
damental one of the tube is produced. This sound is stopped by 
external noises, but goes on again when left undisturbed. All 
these experiments can be made under the ordinary pressure of 
street-gas, # inch of water being sufficient.” 


84 SOUND. 


’ CHAPTER VII. 


ON THH VELOCITY OF TRANSMISSION OF SONOROUS 
VIBRATIONS, AND ON THE MANNER IN WHICH THEY 
AkE PROPAGATED THROUGH ELASTIC BODIES. 


/ 
ON THE SPEED WITH WHICH SONOROUS VIBRATIONS 
TRAVEL. 


WHEN in the country, you have seen a man chopping 
wood. If you stood near him, you observed that the 
blow and the sound of his ax came together. If you 
moved. away from him, you may have noticed that, while 
you could see his ax fall, and hear the sound of the blow, 
the sound seemed to follow the blow. When you moved 
away several hundred feet, the interval of time separating 
the sight of the blow and its sound was readily noted. 
You may also have observed that some time passed be- 
tween the flash of a gun or the puff of a steam-whistle 
and the report of the gun and the sound of the whistle. 
These things convince us that sonorous vibrations take 
time to move through the air. 

This matter has been carefully examined by scientific 
men, and they have found that sound-vibrations move 
through the air at the rate of 1,090 feet (332.23 metres) 
in one second. This is the velocity of sound when the 
temperature is just at freezing, or at 32° Fahrenheit. For 
each degree above this, sound gains in speed one foot more. 


VELOCITY OF TRANSMISSION, ETC. 85 


For instance, upon a summer’s day, the thermometer may 
stand at 80°. This is 48° above 32°, and the sound gains 
48 feet, so that it moves at the rate of 1,138 feet a second 
at this temperature. | 

The velocity of sonorous vibrations in oxygen gas at 
32° is 1,040 feet per second ; in hydrogen gas it is 4,160 
feet, just 4 times as great. Asa cubic foot of hydrogen 
weighs 16 times less than a cubic foot of oxygen, and as 
4 is the square root of 16, it follows that the speed of 
sonorous vibrations in gases varies inversely as the square 
roots of the weights of equal volumes of the gases. 

Sonorous vibrations travel through water at the speed 
of 5,000 feet per second, and through iron at about 16,000 
feet in a second. 


EXPERIMENTS WITH GLASS BALLS ON A CURVED RAILWAY, 
SHOWING HOW VIBRATIONS TRAVEL THROUGH ELASTIC 
BODIES. 


Experiment 55.—Fig. 29 represents a wooden rail- 
way about 6 feet (183 centimetres) long. It may be 
made of pine strips, 14 inch (3.8 centimetres) wide and 4 
inch (6 millimetres) thick, laid side by side about 1 inch 


Fig, 29. 


(25 millimetres) apart, and joined together by short cross- 
strips nailed on them. Get six or seven large glass mar- 
bles at the toy-shop. These are intended to roll be- 


86 SOUND. 


tween the two strips, just as balls roll in the railway of a 
bowling-alley. Place the railway on a table or board, 
and fasten it down at the middle with a screw in the 
cross-strip, and then raise each end and put a book or 
wooden block under it, as in Fig. 29. 

Place the balls in the middle of the curving railway, 
and then bring one to the end and let it roll down against 
the others. Immediately the last ball will fly out and roll 
part way up the incline toward the other end of the rail- 


7 ee 


Fig. 82. 


way. The first ball will come to rest beside the others, 
and the ball which has been shot up the railway will roll 
back against those at rest, and the same performance will 
be repeated till the motion has gone from the rolling balls. 

Let us examine this matter, and see what happens 
to these balls on the railway. First, you must observe 
that the balls are elastic, for experiment will show that 
they will bound like rubber balls when let fall on the 
hearth-stone. 

ExPERIMENT 56.—To show that the ball is elastic, and 
jfiattens when it strikes the stone, make the following ex- 
periment: Mix some oil with a little red-lead, or other 
colored powder, and smear it over a flat stone, like a flag- 


VELOCITY OF TRANSMISSION, ETC. 87 


stone. Rest the ball on this, and observe the size of the 
circular spot made on it. Now let the ball fall on the 
stone, and observe the larger circular spot_made by the 
fall. This shows that when the ball struck it flattened 
and touched a larger. surface.on the.stone.. 

The first ball rolls down and strikes a hard blow on 
the side of ball No. 2. This ball is flattened between 
balls Nos. 1 and 3, as shown in Fig. 30. 

Ball No. 2 at once springs back again into its former 
spherical figure, and in doing so it brings No. 1 to rest 
and flattens No. 3, as shown in Fig. 31. 

Ball No. 3 now springs back into its spherical form, 
and in doing so acts on No. 2 and brings it to rest, and 
acts on No. 4 and flattens it. Thus each ball passes the 
blow on to the next by its elasticity, and each in turn 
flattens and then springs into its natural form, and thus 
we have a series of contractions and expansions running 
through the whole series of balls. The last ball is finally 
flattened, and, when it expands immediately afterward, it 
presses against the ball that gave it the blow and brings 
it to rest; at the same time, finding no resistance in 
front of it, its back-action on the ball behind it causes it 
to start up the railway. Thus the last ball, No 7, is shot 
up the railway by a force derived from ball No. 1, and 
which was sent through all the balls by their successive 
contractions and expansions. | 


EXPERIMENTS WITH A LONG SPRING, SHOWING HOW VI- 
BRATIONS ARE TRANSMITTED AND REFLECTED. 


ExPERIMENT 57.—Obtain a brass wire, wound in the 
form of a spiral spring, about 12 feet long. Get an 
empty starch-box or cigar-box, and take off the cover, 
and then stand it on one end at the edge of a wooden 


88 SOUND. 


table, with the bottom of the box facing outward. Screw 
this box firmly to the table, and then screw a small iron 
or brass hook to the bottom of the box, as shown in Fig. 
33. Slip over this hook the loop at the end of the long 
spiral spring. Hold the other end of the spring in the 
hand, letting it hang loosely between the hand andthe 
box. Insert a finger-nail or the blade of a knife between 
the turns of the wire, near the hand, and pull the turns 


Fre. 33. 


asunder. Free the nail suddenly, and a vibration or 
shock will start and run from coil to coil along the whole 
spring, and a loud rap or blow will be heard on the box, 
thence to be reflected to the hand, and then again to the 
box, and so on. Here we have a beautiful illustration of 
the manner in which a vibration may travel along an elas- 
tic substance, and make itself heard as a sound at the 


VELOCITY OF TRANSMISSION, ETC. 89 


other end, there to be reflected back to the place whence 
it came, to begin over again its forward journey. 


EXPLANATION OF THE MANNER IN WHICH SONOROUS 
VIBRATIONS ARE PROPAGATED. 


If the student clearly understands the actions in the 
experiments with the glass balls and spring-coil, he can 
have no difficulty in perceiving how a shock or vibration 
may in like manner pass through the elastic air. 

For simplicity of illustration, imagine a very long 
tube, in which, at one end, fits a piston or plug. ‘Suppose 
this piston moves quickly forward in the tube through a 
short distance—say, one inch—and then stops. If the air 
were inelastic, then one inch of air would move out of the 
other end of the tube while the piston moved forward one 
inch. But air is elastic ; it gives before the motion of the 
piston ; and it takes some time, after the piston has moved 
forward, before the air moves at the other end of the tube. 
If the tube is 1,100 feet long, and the temperature of the 
air 42°, it will be one whole second before the end of the 
air-column moves ; for it takes that.time for a sound-vi- 
bration to traverse 1,100 feet, and a mechanical action on 
air of the above temperature cannot be sent through it 
with a greater speed than that. 

Now, suppose that the piston takes 4, second to make 
its forward motion in the tube, how far will the air be 
compressed in front of it at the instant the piston stops ? 
Evidently the answer is found by taking +, of 1,100 feet, 
which is 110 feet. If the piston takes ;4, of a second in 
moving forward, then at the end of that time the air is 
compressed before the piston to a depth of 7}, of 1,100 
feet, or 11 feet. The length of the column of air, com- 
pressed by the forward motion of the piston, in every case 


90 SOUND. 


is found by dividing the velocity of sound by the fraction 
of a second during which the piston was moving. 

This compressed air cannot remain at rest in the tube, 
for it is now exactly like the compressed ball “No. 2, of 
Fig. 30. It expands, and in expanding it acts backward 
against the immovable piston, but in front it compresses 
another column of air equal to it in length ; this, in turn, 
acts like ball No. 3 of Fig. 31, bringing to rest the column 
of air behind it and compressing another column in front 
of it ; and in this manner the compression will traverse a 
tube 1,100 feet long in one second. 

If the piston moves backward in the tube, then a col- 
umn of rarefied or expanded air will be formed in front of 
the piston, caused by the air expanding into the space left 
vacant by its backward motion ; and this rarefaction will go 
forward through the air exactly as did the compression. 

Now imagine the piston to move to and fro in the 
tube ; it will send through the column of air condensa- 
tions and rarefactions, following each other in regular 
order. If we have a body vibrating freely in the open 
air, then it will form spherical shells of compressed and 
rarefied air all around it, these shells constantly expand- 
ing outward into larger and larger shells, and following 
each other in regular order and motion, like the regular 
movement of the circular water-waves which spread out- 
ward around a point of agitation on the surface of a pond. 
Thus the sound-vibrations are sent out in all directions 
from a vibrating body just as light is diffused in all direc- 
tions around a luminous body. In our experiments in 
“Tight,” page 34, we found that the illumination of a 
given surface varies in brightness inversely as the square 
of its distance from the source of light. In like manner 
the loudness of a sound decreases inversely as the square 


~ 


VELOCITY OF TRANSMISSION, ETC. 91 


of our distance from the vibrating body. Thus, at 100 
feet, the loudness of the sound is + of what it was at 50 
feet, and at 200 feet its loudness is = of what it was 
when we were 50 feet distant. 

Now what will be the effect on any TO of air— 
like that, for example, which touches the drum-skin of the 
ear—if these condensations and rarefactions reach it? 
Evidently, while the condensations are passing, the mole- 
cules (the smallest parts) of the air will move nearer each 
other, then regain their natural positions, to be separated 
yet farther by the rarefaction which at. once follows. 
Therefore, the effect on any molecule will be to swing it 
to and fro. Hence the air, touching the drum-skin of the 
ear, moves forward and then backward, and forces the 
drum-skin in and then out. This swinging motion is con- 
veyed to the fibres of the auditory nerve, and causes that 
sensation called sound. 

But we have seen that vibrating bodies swing to and 
fro like the pendulum, hence those vibrating bodies which 
are causing sound make all the molecules of air around 
them swing to and fro like the bobs of very small pendu- 


_ lums, each pendulum beginning its swing just a little 


sooner than the one in front of it. 

All this, however, and much more than we have time 
to write about, will be taught you very clearly by an in- 
strument which I shall now show you how to make. 


~ EXPERIMENTS WITH CROVA’S DISK, SHOWING HOW SONO- 


ROUS VIBRATIONS TRAVEL THROUGH AIR AND OTHER 
ELASTIC MATTER. 


ExrERIMENT 58.—In Fig. 34 A is a cardboard disk 
mounted on a whirling machine or rotator B, and C is a 


92 7 SOUND. 


one 


for 


a { fae 
; " yu 
HN mee i 


AIAN APA A 


piece of cardboard having a slit cut in it. Upon the disk 
are 24 eccentric circles drawn with a pen, and so placed 
that they can be seen through the slit in the cardboard. 


VELOCITY OF TRANSMISSION, ETC. 93 


The rotator can be bought of Mr. Hawkridge of Hoboken 
for $3.00 ; the disk you can make yourself from the fol- 
lowing directions : Get a piece of stiff cardboard, and cut 
out a disk 31 centimetres in diameter. In making this 
disk we will use the metric measure exclusively. Round 
the centre C’ of this disk draw a circle just 5 millimetres 
in diameter. (See C, Fig. 35, where it is drawn “full 
size.”) Then divide this circle into 12 parts, and number 
the points of division 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
The next step is to rule upon a sheet of paper a straight . 
line 143 centimetres long, and to mark 72 millimetres of 
this off into 24 spaces of 3 millimetres each, as shown in 
the real size at A B, Fig. 35. This we use as a scale in 
spreading the dividers. Then draw a circle with the di- 
viders spread 74 centimetres, from A to B, Fig. 35, using 
the dot No. 1 at the top of the circle C on the cardboard 
as acentre. Then spread the compasses just 3 millimetres 
wider, using the scale we have just made for a guide, and 
make another circle, with dot No. 2 as a centre. You will 
observe that the two circles are eccentric—that is, they 
are not parallel to each other, one spreading a little to the 
right of the other. Go thus round the circle C twice, and 
use each dot in the circle in turn as a centre till you have 
24 eccentric circles drawn on the disk, each circle having 
a radius 3 millimetres greater than the one next within it. 
When the circles are finished, ink them over with a draw- 
ing-pen holding violet ink, or Indian-ink. When dry, cut 
a small hole exactly in the centre, and mount the disk on 
the rotator. Get a piece of cardboard about 15 centi- 
metres long, and cut in it a narrow slit about 10 centi- 
metres long, in which the eccentric circles will appear 
like a row of dots when the cardboard is held before the 
disk, as in Fig. 34. 


SOUND. 


CROVAS DISK, 


Yop, SIZE. 


Fra. 85. 


VELOCITY OF TRANSMISSION, ETC. 95 


- Now turn the handle of the rotator slowly and steadily. 
The disk will revolve, and the eccentric circles will move 
in the slit in the card. At once you have a most singular 
appearance. A horizontal, worm-like movement among 
the row of dots is seen in the slit. They crowd up 
against each other and then move apart, only to draw 
near again and then separate. ‘There seems to be a wave 
moving along the slit, appearing at one end and disappear- 
ing at the other. At one part of the wave the dots are 
crowding together, at another they are spreading apart. 
Look closely and you will observe that, although this 
wave appears to move over the length of the slit, yet each 
dot makes but a very small to-and-fro movement. No 
matter how fast the crank is turned, or how swiftly the 
waves chase each other along the slit, each dot keeps 
within a fixed limit, swinging to and fro as the waves pass. 

We have learned that the prongs of a tuning-fork vi- 
brate like a pendulum. Both prongs move, but just now 
we will only consider the motion of one. In vibrating it 
swings backward and forward, pushes the air in front of 
it, and gives it a squeeze ; then it swings back and pulls 
the air after it. In this way the air in front of it is alter- 
nately pressed and pulled, and the molecules of air next 
_ to it dance to and fro precisely as the first dot swings to 
and fro behind the slit. You cannot see the motion of 
the molecules of air in front of the tuning-fork, yet our 
apparatus accurately represents their movements so that 
we can leisurely study them. 

First comes an outward swing of the fork, and the air 
before it is squeezed or condensed. Then it swings back, 
and the air before it is pulled apart or spread out ; in 
other words, it is rarefied. So it happens that the fork 


alternately condenses and rarefies the air. The air is elas- 
5 . 


96 _ SOUND. 


tic, and the layer nearest the fork presses and pulls its 
neighbors precisely as described in the previous section, 
where we explained the manner in which sonorous vibra- 
tions are propagated. 

When the fork makes one condensation and one rare- 
faction, it has made one vibration; that is, it has swung 
once to and fro. ‘Then it makes another vibration, and 
produces another condensation and rarefaction. Thus 
condensations and rarefactions follow each other, and 
move away from the fork in pairs, in regular order. 

One condensation, together with its fellow rarefaction, 
forms what is called a sonorous wave. If the fork, for 
example, should vibrate for exactly one second, and then 
stop, the air, for a distance of 1,100 feet all around it, 
will be filled with shells of condensed and rarefied air. 
Therefore, as one vibration to and fro of the fork makes 
one shell of condensed air and its neighboring shell of 
rarefied air, we can find the combined thickness of these 
two shells by dividing 1,100 feet (the velocity of sound) 
by the number of vibrations the fork makes in one second. 
Our A-fork makes 440 vibrations in one second. Hence 
the depth of two shells—one of condensed, the other of 
rarefied air—formed by this fork is 1,100 + 440, which is 
24 feet. The length thus obtained is called a wave-length. 
Evidently, the greater the number of vibrations a second 
the shorter the waves produced. 

Scientific men, to represent a sonorous wave, always 
use a curve like A C O & B of Fig. 36, in which the part 
of the curve A C O, above the line A B, stands for the 
condensed half of the. wave, while the part O & B, below 
A B, stands for the rarefied half of the wave, and the per- 
pendicular height of any part of the curve A C O, above 
the line A B, shows the amount of condensation of the air 


VELOCITY OF TRANSMISSION, ETC. 97 


at that part of the wave ; while similar lines drawn to the 
curve OF B, below A B, show the amount of rarefac- 
tion at these points of the wave. 

The curve A C O & Bis not a real picture of a sono- 
rous wave ; it is merely a good way of showing its length, 
and the manner in which the air is condensed and rare- 
fied in it; for sonorous waves are not formed of heaps 
and hollows like the waves you have seen on the sea. 
They are not heaps and hollows of air, but only conden- 
sations and rarefactions of air. In short, Fig. 36 is merely 
a convenient symbol which stands for a sonorous wave. 


C 


ss 


R 
Fra, 36. 

ExpPrERIMENT 59.—Look at the row of dots seen in the 
slit when the disk is at rest, and find the two dots which are 
- nearest to each other ; this place in the slit corresponds 
to the point Cin Fig. 36. Next find where the dots are 
farthest apart ; this place corresponds to #& in Fig. 36. 
The distance from C to # is one half wave-length ; there- 
fore the distance between two adjoining places, where the 
dots are nearest together, equals the length of one whole 
wave. 


98 SOUND. 


CHAPTER VIII. 


ON THE INTERFERENCE OF SONOROUS VIBRATIONS 
AND ON THE BEATS OF SOUND. 


ExPERIMENT 60.—Cut out two small triangles of cop- 
per foil or tinsel, of the same size, and with wax fasten one 
on the end of each of the prongs of a tuning-fork. Put 
the fork in the wooden block and set up the guide (as in 
experiment, Fig. 21). Prepare a strip of smoked glass, 
and then make the fork vibrate and slide the glass under 
it, and get two traces, one from each prong. 


YING NY MS WADDLE LRP RIRLOS PI IOP II NL LOL LOGS 


INS SF NL NIRS OIE L\IV\I.\ LVI IVIL II SV\IVFINW PINS NS 


Fig. 387. 


Holding the glass up to the light you will see the 
double trace, as shown in Fig. 37. You observe that the 
wavy lines move apart and then draw together. This 
shows us that the two prongs, in vibrating, do not move 
in the same direction at the same time, but-always in op-_ 
posite directions. They swing toward each other, then 
away from each other. 

ExpERIMENT 61.—What is the effect of this movement 
of the prongs of the fork on the air? A ame experi- 
ment will answer this question. 


INTERFERENCE OF SONOROUS VIBRATIONS. 99 


Place three lighted candles on the table at A, B, and 
C (Fig. 38). Hold the hands upright, with the space 
between the palms opposite A, while the backs of the 
hands face the candles Band C. Now move the hands 
near each other, then separate them, and make these mo- 
tions steadily and not too quickly. You thus repeat the 
motions of the prongs of the fork. While vibrating the 
hands observe attentively the flames of the candles. When 
the hands are coming nearer each other, the air is forced 


out from between them, and a puff of air is driven against 
the flame A, as is shown by its bending away from the 
hands. But, during the above movement, the backs of the 
hands have drawn the flames toward them, as shown in 
Fig. 838. When the hands are separating, the air rushes 
- in between them, and the flame A is drawn toward the 
hands by this motion of the air, while at the same time 
the flames at B and C are driven away from the backs of 
the hands. From this experiment it is seen that the space 


100 SOUND. 


between the prongs and the faces_of the prongs of a fork 
are, at the same-instant, always acting oppositely on the air, 

This will be made clearer* by the study of the dia- 
gram, Fig. 39. 


This figure supposes the student looking down on the 
tops of the prongs of the fork. Imagine the prongs 
swinging away from each other in their vibration. Then 
the action of the faces ¢ and ¢ on the air is to condense it, 
and this condensation tends to spread all around the fork. 
But, by the same movement, the space 7 7 between the 
prongs is enlarged, and hence a rarefaction is made there. 
This rarefaction also spreads all around the fork. But, 
as the condensations produced at ¢ and ¢ and the rarefac- 
tions at 7 and 7 spread with the same velocity, it follows 


INTERFERENCE OF SONOROUS VIBRATIONS. 101 


that they must meet along the dotted lines qg, q, q, 4, 
drawn from the edges of the fork outward. The full 
#-circle lines around the fork in Fig. 39 represent the 
middle of the condensed shells of air, while the broken 
4-circle lines stand for the middle of the rarefied shells 
of air. 

Now what must happen along these dotted lines, or, 
rather, surfaces? Evidently there is a struggle here 
between the condensations and the rarefactions. The 
former tend to make the molecules of air go nearer 
together, the latter try to separate them; but, as these 
actions are equal, and as the air is pulled in opposite 
directions at the same time, it remains at rest—does not 
vibrate. ‘Therefore, along the surfaces q, 4g, q, g, there is 
silence. When the prongs vibrate toward each other they 
make the reverse actions on the air ; that is, rarefactions 
are now sent out from cand c, while condensations are 
sent from 7 and 7, but the same effect of silence along 
hs  % 7 18 produced. 

EXPERIMENT 62,—That this is so, is readily proved by 
the following simple experiment. . Vibrate the fork and 
hold it upright near the ear. Now slowly turn it round. 
During one revolution of the fork on its foot, you will 
perceive that the sound goes through four changes. Four 
times it was loud, and four times it was almost if not 
quite gone. Twirl the fork before the ear of a compan- 
ion; he will tell you when it makes the loudest sound, 
and when it becomes silent. You will find that when it 
is loudest the faces ¢, c of the prongs, or the spaces 7, 7 
between them, are facing his ear; and when he tells 
you that there is silence you will find that the edges 
of the fork, that is, the planes qg, 9, g, ¢g, are toward 
his ear. 


102 SOUND. 


AN EXPERIMENT IN WHICH INTERFERENCE OF SOUND IS 
SHOWN BY ROTATING A VIBRATING FORK OVER THE 
MOUTH OF A BOTTLE RESOUNDING TO THE NOTE OF 
THE FORK. 


EXPERIMENT 63.—Get a bottle, like one of those shown 
in Fig. 40, holding about 5 fluid ounces when filled to its 
brim. Its mouth should measure 1 inch (25 millimetres) 
in diameter. Cut a piece of glass 1} inch long and 1 inch 
wide, and slide this over the mouth of the bottle while 
the vibrating A-fork is held over it. Fix the piece of 
glass with wax at the place where it makes the air in the 
bottle resound the loudest (see Fig. 40). 

Again vibrate the fork, and holding it horizontally 
twirl it slowly over the partly closed bottle, just as we 
twirled it before the ear. You will find that whenever 
the corners of the fork have come opposite the mouth of 
the bottle the sound will have faded away to silence. In 
this position of the fork, one of the planes q, q, ¢g, or q, of 
Fig. 39, goes directly down to the mouth of the bottle, 
and therefore there enter the bottle, side by side, at the 
same time, a condensation and a rarefaction. Hence the 
air in the bottle is acted on by two equal and opposed ac- 
tions ; it cannot vibrate to the fork, and we have rest 
and silence. The above experiment, and the following 
one, may be made as well with the tuned tumblers of 
Experiment 43 as with the bottles. 


“ EXPERIMENTS IN WHICH INTERFERENCE OF SOUND IS OB- 
TAINED WITH A FORK AND TWO BOTTLES. 


EXPERIMENT 64,—Fig. 40 represents two glass bottles, 
of equal size, and each tuned as described in Experiment 


INTERFERENCE OF SONOROUS VIBRATIONS. 103 


63. Set one bottle upright, and with two bits of wax 
hold the other horizontally on some books, with the mouths 
of the bottles nearly touching, as shown in Fig. 40. 

Make the fork vibrate, and, holding it horizontally, 
bring it down so that the space between the prongs will 
be opposite the mouth of the upright bottle, as shown in 


Fie. 40. 


Fig. 40. As it descends, you will observe that the sound 
first increases, and then suddenly fades away or entirely 
- disappears. You can raise the fork and hear it still sound- 
ing, so that you may be sure it has not stopped, and yet, 
in a certain position between the two bottles, the sound is 
nearly if not wholly lost. 


104 SOUND. 


In this experiment, you will observe that while the face 
of one of the prongs is opposite the mouth of one bottle 
the space between the prongs is opposite the mouth of the 
other bottle. Therefore, while one bottle receives a con- 
densation the other receives a rarefaction. Thus opposed 
vibratory motions issue from the mouths of the bottles, 
and they neutralize each other’s action on the outside air. 
Hence silence is observed when the fork is in such posi- 
tion that the condensation or rarefaction which comes out 
of one bottle exactly equals in power the rarefaction or 
condensation which comes out of the other bottle. 

You know that the air is really resounding in the bot- 
tles, even when silence is outside of them, by the fol 
ing simple experiments : 

EXPERIMENT 65.—Slip a piece of cardboard over the 
mouth of one of the bottles, and at once the other bottle 
resounds to the fork and sings out loudly. The balance 
is thus broken and sound is heard. 

EXPERIMENT 66.—A piece of tissue-paper will pro- 
duce another effect, because it is thin and only partly cuts 
off the vibrations, and the result is a feeble sound ; partly 
an interference and partly a free action of the condensa- 
tions and rarefactions, half silence, half sound. 


EXPERIMENT SHOWING REFLECTION OF SOUND FROM A 
FLAT GAS-FLAME, 


EXPERIMENT 67.—By a little care you can even slide 
the flat flame of a fish-tail gas-jet before the mouth of the 
horizontal bottle, and thus make a flame act as a guard to 
stop the vibrations from entering the bottle. 

When two sonorous vibrations meet and make silence, 
they are said to “interfere.” ‘The experiments just made 
are experiments in the interference of sound. 


INTERFERENCE OF SONOROUS VIBRATIONS. 105 


EXPERIMENTS IN WHICH, BY THE AID OF A PAPER CONE 
AND A RUBBER TUBE, WE FIND OUT THE MANNER IN 
WHICH A DISK VIBRATES. 


In describing Experiments 27, 28, 29, and 30, we stated 
that a vibrating disk always divided itself into an even 
number of sectors. This fact was explained by the state- 
ae that the adjoining vibrating sectors of the disk were 

always moving in opposite directions. The truth of this 
ae will be manifest on making the following ex- 
periments, which can only be explained by the fact that 
adjoining sectors, at the same instant, are always in oppo- 
site phases of vibration. These experiments will also 
afford beautiful illustrations of the interference of sono- 
rous vibrations. ; 

Take a piece of cardboard and roll it into a cone about 
10 inches long. The small end of the cone should have in 
it an opening of such a size that the cone will fit into the 
rubber tube used in Experiment 32. If a brass disk of 6 
inches in diameter is used in the experiments, the mouth 
of the cone should be 24 inches in diameter. 

EXPERIMENT 68.—Make the plate vibrate with four 
sectors as in A, Fig. 23. Close one ear with soft wax ; into 
the other put the end of the rubber tube ; then place the 
centre of the mouth of the cone exactly over the centre of 
the plate with the cone quite close to its surface. In this 
position (which we will call No. 1, for future reference) no 
sound is perceived, or at least only a very faint one. This 
is so, because in this position of the cone it always receives, 
at the same instant, from the vibrating disk, four equal 
sound-pulses ; and as two of these are condensations, and 
two are rarefactions, they mutually neutralize each other, 


106 SOUND. 


and the drum-skin of the ear remains at rest and no sound 
is perceived. 

ExpERIMENT 69.—Now move the mouth of the cone 
along the middle of a vibrating sector toward the edge 
of the disk. As the cone progresses the sound grows 
louder till it reaches its maximum when the edge of the 
cone reaches the edge of the disk. In this position (No. 
2) the cone receives from the disk only regular sonorous 
vibrations, one condensation or one rarefaction alone enter- 
ing the disk at a time. 

EXPERIMENT 70.—Slowly move the cone along the 
circumference of the vibrating disk, keeping the edge of 
its mouth close to the border of the disk. The sound at 
once begins to diminish in intensity, until the circle of the 
mouth of the cone in its progress is divided into two 
semicircles by a nodal line. No sound is now perceived, 
because in this position (No. 3) a condensation and a rare- 
faction enter the ear together, for on the opposite sides of 
a nodal line the plate has always opposite directions of 
motion. : 


EXPERIMENTS WITH BEATING SOUNDS. 


~ Exprertment 71.—In purchasing the two A-forks, you 
took special pains to get two which were tuned accurately 
to unison; otherwise they are of: no value for our experi- 
ments. ‘lake one of these in each hand and make them 
sound together. Hold them near each other close to the 
ear, and you will observe that while both sound there ap- 
pears to be but one note. The two sounds blend together 
perfectly, so that we cannot distinguish one from the 
other. Having tried this thoroughly, place a bit of wax 
on the end of one of the forks, and then make them sound 


INTERFERENCE OF SONOROUS VIBRATIONS. 107 


while each is held upright on its resonant box (see Experi- 
ment 41). At once you hear something unusual: little 
bursts of sounds, followed by sudden weakenings and loss 
of power, as if the forks sang forte and then piano alter- 
nately. These singular quivering changes in the tone of 
the two forks, when sounded together, are called “ beats.” 
The sound seems to beat with a pulse-like motion at regu- 
lar intervals. Take off the wax and the beats disappear, 
and the two forks sound together like one instrument. 

EXPERIMENT 72.—Put on a larger or smaller piece of 
wax and the beats change their character, coming faster 
or slower each time the amount of wax is changed. 

These experiments succeed admirably by using the 
tumblers of Experiment 43, or the resonant bottles of Ex- 
periments 63, 64, in place of the resonant boxes. The 
tumblers or bottles should be carefully tuned, one to the 
loaded, the other to the unloaded fork. 

To understand these singular beats, you must remem- 
ber that each fork sends out sonorous waves, or alternate 
condensations and rarefactions, through the air. When 
the forks are sounded together (without the wax), each 
sends out the same number of waves in a second, and 
these travel out together, the condensations and rarefac- 
tions of each moving side by side, and reaching the ear 
at the same time. 

When we loaded one fork with wax we caused it to 
move slower. The processions of waves streaming out 
from each may start together, but they do not keep to- 
gether ; as the loaded fork is going slower its waves of 
sound are longer and drag behind. The condensations 
and rarefactions no longer travel side by side. A con- 
densation from one fork arrives at the ear at the same 
time that a rarefaction arrives from the other. Thus 


108 SOUND. 


they interfere and destroy each other, and the interfer- 
ence makes silence, just as we discovered in our last ex- 
periments. The condensations and rarefactions from the 
two forks continue to arrive at the ear, and soon two con- 
densations or two rarefactions come side by side and ar- 
rive at the ear together, and they mutually aid or reén- 
force each other, and there is a sudden burst of sound as 
if the forks were sounding louder. 

The waves of sound continue to move, and one set of 
waves slips past the other, till the condensations of one set 
arrive at the ear alongside of the rarefactions of the other, 
and again there is interference and silence. By such con- 
tinuous actions beats of sound are produced. 


Fie. 41. 


Fig. 41 represents two such series of waves traveling 
side by side. One series is represented by a full line, the 
other by a dotted one. At A the condensations of one 
series are shown as opposite the rarefactions of the other ; 
but, as the waves represented by the full line are longer 
than those represented by the dotted line, the former pass 
the latter, so that at C the two series act together, and 
we have a beat ; while at a more distant point, B, the 
motions in the waves are opposed, and here there is inter- 
ference and silence. It is evident that the sliding of the 
longer waves past the shorter will cause the waves, meet- 


INTERFERENCE OF SON OROUS VIBRATIONS. 109 


ing at B, alternately to act together and to interfere ; and 
thus the ear, placed at , will perceive beats of sound. 

It necessarily follows that, if one fork vibrates 100 
times in a second and the other 101 times, there will be 
one beat in every second. The number of beats made in 
a second is equal to the difference in the number of vibra- 
tions per second made by the two vibrating bodies. 


oO 
a A 


110 SOUND. 


CHAPTER IX. 
ON THE REFLECTION OF SOUND. 


PROFESSOR ROOD’S EXPERIMENT, SHOWING THE REFLEC- 
TION OF SOUND. 


EXPERIMENT 73.—Fig. 42 represents a disk of card- 
board 12 or 14 inches in diameter, and having two sectors 
cut out of it, on opposite sides of its centre. This is 
mounted on the rotator, so that it can be turned round 
quickly. Let some one sit beside the rotator so that 
he can turn the handle, and at the same time blow a toy 
trumpet, which I have found to be the best pipe for this 
experiment. Hold the trumpet so that it will be inclined 
to the surface of the disk, and with its open end just in 
front of one of the openings, as shown in Fig. 42. While 
the rotating disk is being turned steadily round, and the 
pipe is sounding, go to a distant part of the room, and | 
here you will perceive the sound of the pipe changing 
rapidly, alternately growing louder and then softer like 
beats. 

This effect is the result of reflection. When the solid 
part of the disk passes before the pipe the vibrations of 
sound are reflected or echoed from the card. When the 
openings pass before the pipe, part of the vibrations pass 
through the open place and are lost, and the sound to the 
listener appears to lose power. 


REFLECTION OF SOUND. 111 


In performing this experiment care must be taken to 
place the disk in such a position that the sound will be 
reflected to the distant listener. As we learned in our ex- 


ZZ 


Z 
ZZ 
Z, 


periments in “ Light,” there is a law governing reflections. 
We found by our experiments that the angle of reflection 
is always equal to the angle of incidence, and the same 
law holds good in the reflection of sound. 

ExprerimEent 74.—Another experiment in the reflec- 
tion of sound may be made with a common palm-leaf fan. 
Let some one sound the trumpet at one end of a room, 
while you hold the fan upright beside one ear. While 


< 


112 SOUND. 


the trumpet is sounding, twirl the fan slowly by the han- 
dle, and you will observe a change in the sound. In cer- 
tain positions of the fan the trumpet will sound louder, 
and in other positions it will be softened. If you do not 
obtain this effect at once, try the fan in several positions 
as it stands upright, and, after a few trials, you will ob- 
tain a reflection of the sound from the surface of the fan. 
The sound of a locust on a warm day, or the beating of 
the surf on the shore, or the sound of a distant voice, may 
thus be caught on the fan and reflected into the ear. 

Echoes are also reflections. The vibrations travel 
through the air and meet a building, then the side of a 
mountain or hill, and rebound or reécho, perhaps many 
times. 

EXPERIMENT 75.—You can readily find an echo any- 
where in the country by walking near a barn or house and 
shouting or singing. The first trial may not bring out 
the echo, but, by changing your position, going nearer or 
walking farther away, and always standing squarely in 
front of the barn or other building, you will soon find the 
spot where an echo is heard. We already know that in 
winter, when the thermometer is at 82° Fahr., sound 
moves at the rate of 1,090 feet in a second. If you stand 
at 545 feet from the reflecting wall, and make a short, 
sharp sound, it will take one half second for it to go to the 
wall, and one half second to come back, and there will be 
one second between the sound and its echo. 

In our experiments with the tuning-fork and two bot- 
tles (see Fig. 40), you remember, we put a piece of card- 
board and a flat gas-flame before the mouth of one of the 
bottles. Here, also, we had a reflection of the sound from 
the cardboard, and even from the flame. 


ad 


PITCH OF SOUNDS. 1138 


CHAPTER X. 
' ON THE PITCH OF SOUNDS. 


ExprerimmMEnt %6.—Take one of the A-forks and the C- 
fork and stick them in the block of wood side by side, 
with the opposite prongs of the two forks inclined to 
each other, so that by drawing a rod between them they 
* will be set vibrating at the same time. Stick a piece of 
copper-foil on the tips of the prongs nearest each other, 
and arrange the smoked glass and its guide as directed in 
Experiment 25. Vibrate the forks by drawing the rod 
between them, and obtain the traces of their vibrations on 
the smoked glass. 

Take the smoked glass and carefully measure off an 
equal space on each trace, and then count the vibrations 
inclosed in this space. If the right forks have been se- 
lected it will be found that 174 vibrations of one fork 
cover as much space.as 21 vibrations of the other. From 
this you readily see that, in the same time, one fork vi- 
brates oftener than the other. Carefully notice which 
fork makes the greater number of vibrations. Bring one 
vibrating fork to the ear, and then the other, and you will 
observe that the C-fork gives a higher note than the A. 
The C-fork makes the greater number of vibrations (21) 
in a given length on the trace, and the A-fork makes the 
smaller number (174) in the same length. We are con- 


114 SOUND. 


vinced by this experiment that a fork giving a high note 
vibrates oftener in a second than a fork giving a lower 
note. Experiments on all kinds of vibrating bodies— 
solids, liquids, and gases—have proved that the pitch of a 
sounding body rises with the increase in the number of 
its vibrations in a second. This fact may be stated thus: 
The pitch rises with the frequency of the vibrations. 
From the above fact it follows that the pitch of a sound 
rises with an increase in the number of sonorous waves 
that reach the ear in a second. 


EXPERIMENTS WITH THE SIREN. 


Fig. 43 shows an instrument called a siren. I will 
show you how to make several instructive and curious 
experiments with it. First, you will find out the number 
of vibrations made in a second by a sounding body like 
one of your tuning-forks ; and, having found out this, 
you will use the fork to determine for yourself the veloc- 
ity of sound. The siren will also tell you this important 
fact: That the numbers of vibrations per second which 
give the various notes of the gamut, or musical scale, bear 
_ to each other fixed numerical relations. 

To make the siren, get a piece of cardboard, or mill- 
board, and draw on it with a pair of dividers a circle 
83 inches (21.6 centimetres) in diameter; then cut this 
circle out of the cardboard. Now draw four circles, the 
inner one with the legs of the dividers opened to 2} inches 
(5.73 centimetres), the next with a radius of 22 inches 
(6.99 centimetres), the third with 34 inches (8.26 centi- 
metres), and the fourth with 33 inches (9.53 centimetres). 
Divide the circumference of the outer circle into 24 equal 
parts, and to each of these points of division draw a line 
from the centre, as shown in Fig. 44. Divide the spaces 


PITCH OF SOUNDS. 115 


on the outer circle in halves; this will give 48 points on | 
this circle. At each of these points cut a hole of about 


a iV 


Well 
v1 

an LATTaae 3 
—_ = 


a 


7s Inch (5 millimetres) in diameter with a punch. Then 
punch holes at the 24 points on the inner circle. 

The student, on looking at Fig. 44, will see that, on 
the radii marked 1, 2, 3, 4, 5, and 6, the holes are all in a 


116 SOUND. 


line. These holes, thus in line, divide the circle into six 
equal parts. Divide each of these sixths on the second cir- 
cle into five equal parts, and each sixth on the third circle 
into six equal parts, and through each of these points of 
division cut a hole with the punch. By following these 


directions you will have made on the inner circle 24 
holes, on the second 380, on the third 36, and on the fourth 
48 holes. 

Now cut a hole in the centre of’ the disk, so that it 
neatly fits on the screw of the small pulley of the rotator 


PITCH OF SOUNDS. 117 


shown in Fig. 43. Then put into a piece of India-rubber 
tube a glass tube having its interior about the diameter 
of the holes in the card disk. We are now ready for our 
experiments. 

EXPERIMENT 77.—Rotate the disk slowly, and, placing 
the glass tube before a ring of holes, blow through the 
tube. You will observe that whenever a hole comes be- 
fore the tube a puff of air goes through the disk. If the 
disk is revolved faster the puffs become more frequent, 
and soon, on increasing the velocity of the disk, they blend 
into a sound. Not very pure, it is true; but yet, in the 
midst of the whizzing, your ear will detect a smooth note. 
Fixing your attention on this note, while the rotator is 
urged with gradually increasing velocity, you will hear 
the note gradually rising in pitch. This again shows us 
that the pitch of a sound rises with the frequency of the 
vibrations causing it. 

Two bodies make the same number of vibrations in a 
second when they give forth sounds of the same pitch. 
Therefore, if we can measure how many vibrations the 
disk makes in a second while it gives the exact sound of 
one of the forks, we will have measured the number of 
vibrations which the fork makes in asecond. If we count 
with our watch ‘the number of turns the crank C makes in 
one minute, we can from this knowledge calculate the 
number of puffs or vibrations the disk makes in one sec- 
ond, as follows: One revolution of the crank of the rota- 
tor makes the disk go round exactly five times. Now, 
suppose that the tube is before the third circle, having 86 
holes, and that in. one minute the crank C turns round 
100 times. Then in one minute the disk turned 5 times 
100 times, which is 500 times. But for each turn of the 
disk 36 puffs or vibrations were made on the air ; there- 


118 SOUND. 


fore, 36 times 500, or 18,000, puffs or vibrations were 
made by the disk in one minute, and 7, of 18,000, or 300, 
in one second. 

But it is difficult to know just when the disk gives the 
same sound as the fork, and it is yet more difficult to keep 
the disk moving so that it holds this sound, even for a few 
seconds. ‘To do this, very expensive apparatus has here- 
tofore always been needed. But I did not wish to ban- 
ish from our book such an important experiment, so I 
found out a cheap and simple way of doing it, which I 
will show you. 


EXPERIMENT WITH THE SIREN, IN WHICH -IS FOUND THE 
NUMBER OF VIBRATIONS MADE BY A TUNING-FORK IN 
ONE SECOND. 


ExPERIMENT 78.—Get a glass tube (the same we used 
in the experiment on page 50 of “ Light ”) # inch (19 milli- 
metres) in diameter and 12 inches (30.5 centimetres) long, 
-and a cork 1 inch thick, which slides neatly in the tube. 

Put the cork into one end of the tube, and holding a stick 
upright press the cork down on it. The fork is now vi- 
brated and held over the open end of the tube, while the 
cork is forced up the tube with the stick till the column 
of air in the tube is brought into tune with the fork. 
This you will know by the tube sending out a loud sound. 
Try this several times till you are sure of the exact place 
~where the cork should be to make the tube give the loud- 
est sound. 

Now lay the fork aside, and with small pieces of wax 
stick the tube on the top of a block, or on a pile of books, 
with its mouth near the disk and facing one of the cir- 
cles of holes, as shown in Fig. 43. On the other side 


PITCH OF SOUNDS. 119 


of the disk, and just opposite the mouth of the resonant 
tube, hold the small tube through which you blow the air. 

Turn the crank at first slowly, then gradually faster 
and faster. Soon a sound comes from the tube. This 
gets louder and louder ; then, after the disk has gained a 
certain speed, the sound grows fainter and fainter, till no 
sound at all comes from the tube. 

When the sound from the tube was the loudest, the 
disk was sending into the tube the same number of vi- 
brations in a second as the fork makes ; for the tube was 
tuned to the fork, and can only resound loudly when it 
receives from the disk of the siren the same number of 
vibrations in a second as the fork gives. 

It is, then, quite clear that, to find out the number of 
vibrations per second given by the fork, we first have to 
bring the disk to the velocity that makes the tube sound 
the loudest, and then to use this sound as a guide to the 
hand in turning the crank of the rotator. Practice will 
soon teach the hand to obey the check given by the ear ; 
_ and if the student have patience, he will be rewarded when 
he finds that he can keep the tube: sounding out loudly 
and evenly for 20 or 30 seconds. Then we count the 
number of turns made by the crank-handle OC of the rota- 
tor in 20 or 30 seconds of the watch. If we have suc- 
ceeded in this, we can at once calculate the number of 
vibrations the fork makes in one second. 

The following will show how this calculation is made : 

Experiment 79.—The cork was pushed to that place 
which made the air in the tube resound the loudest to the 
A-fork. The tube was then placed facing the circle of 36 
holes. After we had succeeded in making the tube re- 
sound loudly.and evenly to the turning disk, I counted the 


number of turns I gave to the handle C in 20 seconds, 
6 


120 SOUND. 


and I found this number to be 49. For one revolution of 
the handle C, the disk makes exactly five. Hence 5 times 
49, or 245, is the number of turns the disk made in 20 sec- 
onds. But in one turn of the disk 36 puffs or vibrations 
entered the tube; therefore, 245 times 36, or 8,820, is the 
number of vibrations that went into the tube in 20 sec- 
onds; and 3, of 8,820, or 441, is the number of vibra- 
tions which entered the tube in one second. 

The experiment, therefore, shows that the tube resounds 
the loudest when 441 vibrations enter it in one second. 
But the tube also resounded its loudest when the vibrating 
A-fork was placed over it. Hence the A-fork makes 441 
vibrations in one second. ; 

ExpPERIMENT 80.—Let the student now try to find out 
by a like experiment the number of vibrations made by 
the C-fork in one second. Repeat these trials many times 
till numbers are found which do not differ much from one 
another. 


' FINDING THE VELOCITY OF SOUND BY AN EXPERIMENT 
WITH THE TUNING-FORK AND THE RESONANT TUBE. 


ExpERIMeNT 81.—Our experiment (78) with the glass 
tube has taught us that the tube must have a certain depth 
of air in it to resound loudly to the A-fork. Let us meas- 
ure this depth. We find it to be 7% inches (19.47 centi- 
metres) when the air has a temperature of 68° Fahr. 

From this measure, and from the knowledge that the 
A-fork makes 441 vibrations in one second, we can com- 
pute the velocity of sound in air. 

It is evident that the prong of the fork over the mouth 
of the tube, and the air at the mouth of the tube, must 
swing to and fro together, otherwise there will be a strug- 


PITCH OF SOUNDS. 121 


gle and interference between these vibrations, and then 
the air in the tube cannot possibly co-vibrate and strengthen 
the sound given by the fork. — 

We have already learned that the prong of the fork 
in going from a to b, Fig. 45, makes one half wave-length 
in the air before it. This may be represented by the 
curve 6 cd above the line 6 d. Now the tube 7’ must be 
as long as from 6 to ¢, or one-quarter of a wave-length ; 
so that, by the time the prong of the fork has gone from 
a to b, and is just beginning its back-swing from 6 to a, 


Fig, 45. 


the half-wave 6 c d has just had time to go to the bottom 
of the tube 7; to be reflected back, and to reach the prong 
b at the very moment it begins its back-swing. If it does 
this, then the end of this reflected wave (shown by the 
dotted curve in the tube 7’) moves backward with the 
back-swing of the prong 0, and thus the air at the mouth 
of the tube and the prong of the fork swing together, and. 
the sound given by the fork is greatly strengthened. 

If the depth of the quarter of the wave made by the 
A-fork is 7% inches (19.47 centimetres), the whole wave is 


122 SOUND. 


30.64 inches, or 2.55 feet (77.88 centimetres). But we 
have already learned that, when the A-fork has vibrated 
for one second, it has spread 441 sonorous waves all 
around it. As one wave extends 2.55 feet (77.88 centi- 
metres) from the fork, 441 waves will extend 441 times 
2.55 feet (77.88 centimetres), or 1,124 feet (342.6 metres). 
This is the distance the vibrations from the A-fork have 
gone in one second. In other words, this is the velocity 
of sound in air at 68° Fahr., as found out by the fork and 
resonant tube. 

Thus we find that the most modest apparatus, when 
used with patience and thoughtfulness, can solve problems 
which, at first sight, may appear far beyond our power. 
The cardboard siren, the little tuning-fork, and the glass 
tube have measured the number of vibrations of the fork 
and the velocity of sound. 

EXPERIMENT 82.—In a similar manner let the student 
determine the number of vibrations of the C-fork, and 
then with it and the resonant tube let him measure the 
velocity of sound, and compare this result with that found 
with the A-fork. 


' THE NUMBER OF VIBRATIONS PER SECOND, GIVEN BY RES- 
ONANT TUBES AND ORGAN-PIPES, IS INVERSELY AS 
THEIR LENGTHS. 


If the number of vibrations per second of the fork be 
doubled, the sonorous waves which it makes will be short- 
ened one-half; hence the resonant tube must be shortened 
one-half in order to resound to the fork. If the num- 
ber of vibrations of the fork are half as frequent, it will 
make sonorous waves twice as long ; hence the tube to re- 
sound to this fork must be doubled in length. These facts 


PITCH OF SOUNDS. 123 


are stated in the following law: The lengths of resonant 
tubes are inversely as the numbers of the vibrations to 
which they resound. 

But organ-pipes are merely resonant tubes whose col- 
umns of air, instead of being vibrated by a tuning-fork, 
are vibrated by wind passing through a mouth-piece ; 
hence the following law: The lengths of organ-pipes are 
inversely as the numbers of vibrations which they give in 
a second, . 


124 | SOUND. 


CHAPTER XI. 


ON THE FORMATION OF THE GAMUT. 


EXPERIMENTS WITH THE SIREN, SHOWING HOW THE SOUNDS 
OF THE GAMUT ARE OBTAINED. 


Tue disk of our siren has four circles of holes. The 
innermost or first circle contains 24 holes, the second. 30, 
the third 36, and the fourth or outermost circle has 48 
holes. 

EXPERIMENT 83.—Turn the handle of the rotator even- 
ly and steadily, and at a moderate speed, and, while 
blowing through the tube, move it quickly from the 
inner ring of holes to the next, then to the next, and 
finally to the outer ring of holes. No experiment yet 
made brings so pleasant a surprise as this one. We 
have already found that the pitch of sound rises with 
the increase in the frequency of the vibrations caus- 
ing it. As the tube moves from the first to the fourth 
circle, more holes successively pass before it in one turn 
of the disk ; therefore the pitch rises suddenly as the tube 
reaches each circle in order. But, more than this, the 
successive sounds evidently have a familiar musical rela- 
tion to each other, and this musical relation is not changed 
by turning the disk more or less rapidly. The pitch of 
the notes is thereby changed, but the same musical rela- 


FORMATION OF THE GAMUT. 125 


tion exists no matter how swiftly the disk turns during 
the experiment. 

EXPERIMENT 84,—A few trials will convince you that, 
when you sing the notes DO, MI, SOL, DO, you produce 
sounds which follow each other with precisely the same 
musical intervals as when you blow air in order through 
the 24, 30, 36, and 40 holes in the disk. You have reached 
a grand truth lying at the very foundation of music. 
Your experiment tells you that, if four sounds are made 
by vibrations whose numbers per second are as 24: 30: 
36: 48, then these sounds will be those of four notes 
which bear to each other the same musical relation as 
exists among the notes DO, MI, SOL, DO. In other words, 
these four sounds will be the four sounds of what musicians 
call the perfect major chord. 

Examining the numbers 24, 30, 36, and 48, we see that 
each of them may be divided by 6. Doing this, we obtain 
the four numbers 4, 5, 6,and 8. The ratios 4:5:6:8 are 
the same as held among the other numbers, but are simpler 
and easier to remember. Thus the perfect major chord 
will always be produced, if the ratios of the vibrations per 
second of four sounds are as 4:5:6: 8. 

EXPERIMENT 85.—By blowing first into the circle of 
24 holes and then into the circle of 48 we hear two notes. 
The second is the octave of the first, and the fact is uni- 
versally true that the octave of any sound is obtained by 
doubling the number of its vibrations. 

With our siren we have just found out the relations of 
the numbers of vibrations per second which make the four 
sounds of the perfect major chord. But this simple instru- 
ment has even greater capacity than this. It can give us 
those related numbers of vibrations which form all the 
sounds of the gamut. 


126 SOUND. 


From the proportion 4 : 5 : 6 are derived all the sounds 
of the musical scale. These numbers form the very 
foundations of harmony. ‘They should be engraved on 
the pediment of the temple of music. 

It has been discovered by experiment that the numbers 
of vibrations giving the notes of the gamut, or, more 
properly, the sounds of the natural scale of music, are re- 
lated as is shown in the following proportions : 

(1)? te OO: Ce tk ssa. 
(2) “pe 2) -ohOuue fare cts sale 
(3) 46 De-4 cic A ae, 

Small c and d stand for the notes of the octave above 
C and D. 

To form the gamut from these proportions, we must - 
decide on the number of vibrations per second which 
shall give the sound C or DO. Let 264 vibrations per 
second be fixed as giving the C or DO of the octave below 


Then Proportion (1) becomes 
C:E:G::4:5:6: : 264: 330: 396, 
Proportion (2) becomes 
G:B:d:34:5: 6% : 396: 495 : 594. 
Proportion (3) becomes 
Ct AL Bi) 6:25 4) 528 24400 352, 

Thus, by starting the first number of Proportion (1) 
with C, equal to 264 vibrations, we find that G will be 
given by 396 vibrations. Then starting Proportion (2) 
with G, equal to 396 vibrations, we find that B and the 
octave above D will be given by 495 and 594 vibrations. 


FORMATION OF THE GAMUT. 127 


Therefore D is equal to one-half of 594, or 297. We start 
Proportion (8) with c, of 528 vibrations, the octave above 
C, and we obtain the numbers of vibrations per second 
which give the sounds A and F, 

We here write in their proper order these notes of the 
gamut, and place under them their numbers of vibra- 
tions. The notes of the gamut are also designated as Ist, 
2d, 3d, 4th, etc., so as to indicate what are called znter- 
vals, ‘Thus the G forms to the C the interval of the 5th. 
The E is the interval of the 3d to C. 


—— SS 


ee Ae 
264 297 330 352 396 440 495 528 
1st 2d 3d 4th Sth 6th ‘7th 8th. 

An examination of these numbers will show that each 
may be divided by eleven. Doing this, we obtain the fol- 
lowing series of numbers, which gives the relative numbers 
of the vibrations for the notes of the gamut in any octave 
of the musical scale : 

Cre lor Wie Gee Asch Dia C 
24: 27: 30: 832: 36: 40: 45: 48. 

ExprRIMENT 86.—Of the correctness of the above 
mode of forming the gamut, you may convince yourself 
by cutting another disk for the siren having eight in- 
stead of four circles of holes, each circle having, in order, 
these numbers of holes, viz.: 24, 27, 30, 32, 36, 40, 45, 48. 
Turning the disk, by giving to the crank a uniform mo- 
tion of 22 revolutions in 10 seconds, while you succes- 
sively blow into the circles, you will hear in succession 
the eight notes of the gamut of the octave of C, of 264 
vibrations, 


128 SOUND. 


EXPERIMENT 87.—Even the disk with four circles of 
holes may be made to give all the notes of the gamut, but 
only four notes in each experiment. 

You will find on making the calculation that, if you 
turn the handle of the rotator 22 times in 10 seconds, you 
will make the C of Proportion (1); 33 turns in 10 seconds 
will give the G of Proportion (2); while 294 turns in 10 
seconds will give the F of Proportion (3). Hence, if you 
blow into the four circles of holes, while the disk has in 
succession these three different velocities, you will succes- 
sively get the numbers of vibrations making the sounds 
of the gamut given in Proportions (1), (2), and (8). 


EXPERIMENTS WITH THE SONOMETER. 129 


“ CHAPTER XII. 


| EXPERIMENTS WITH THE SONOMETER, GIVING THE 
SOUNDS OF THE GAMUT AND THE HARMONICS. 


Fic. 46 represents a wooden box 59 inches (150 centi- 
metres) long, 43 inches (12 centimetres) wide, and 43 
inches (12 centimetres) deep. The sides are made of oak 


Fie. 46.—The Sonometer. 


$4 inch (12 millimetres) thick, and the two ends of oak 
1 inch (25 millimetres) thick. These are carefully dove- 
tailed together. In the side-pieces are cut three holes, as 
shown in the figure. There is no bottom to the box, and 
the top is made of a single piece of clear pine 4 inch (3 
millimetres) thick, and glued on. Two triangular pieces, 
4 inch (2 centimetres) high, and glued down to the cover 
of the box, just 474 inches (120 centimetres) apart, form 
bridges over which the wires are stretched. There is 
also, as shown at Z, a loose piece of pine 24 inches (6.35 


130 SOUND. 


centimetres) wide, 4 inch (2 centimetres) thick, and about 
43 inches (12 centimetres) long. At a, 6 are two screw- 
eyes set firmly upright at one end of the box in the oak. 
At c,d are two piano-string pegs. From these to the 
screw-eyes are stretched two pieces of piano-forte wire 
(No. 14, Poehlemann’s patent, Nuremberg). In putting 
on these wires, the ends must be annealed, by making 
them red-hot in a stove, before they are wound round the 
screw-eyes or pegs. Such an instrument is called a so- 
nometer, and will make a useful and entertaining instru- 
ment for our experiments. When it is finished, the wires 
may be drawn up tight by means of a wrench or piano- 
tuner’s key, and then we shall find, on pulling the wire 
one side and letting it go, that it gives a clear tone that 
lasts some time. 


EXPERIMENTS WITH THE SONOMETER, GIVING THE SOUNDS 
OF THE GAMUT. 


ExPERIMENT 88.—Place the sonometer (Fig. 46) in front 
of you, and with a metric measure lay off distances from 
the left-hand bridge to the right, of 60 and 30 centimetres, 
Tighten the wire till it gives, when plucked, a clear musical 
sound, not too high in pitch. Then place the block # 
(Fig. 46) under the wire, with its edge on the line marked 
60 centimetres, and place the end of the finger on the wire 
at this edge of the block. Pluck the wire at the middle 
of this length of 60 centimetres, and listen attentively to 
the pitch of the sound. Then at once remove the block 
and pluck the wire in its middle so that the whole wire 
vibrates. You will perceive that the sound now given 
is like the one given when the half-wire vibrated, only it 


EXPERIMENTS WITH THE SONOMETER. Ist 


differs in this, it is the octave below it. With the block 
placed at 30 centimetres, vibrate one-quarter of the length 
of the wire, and you will find that we have the sound 
of the first octave above that made by half the wire, 
and the second octave above the sound given by the 
whole wire. 

Our siren has proved that by doubling the number of 
vibrations the sound rises an octave. Therefore, when a 
wire is shortened one-half -it vibrates twice as often, and 
when shortened one-quarter it vibrates four times as often, 
as when its whole length vibrates. This then is the rule, or 
law, which governs the vibrating wire. The force stretch- 
ing the wire remaining the same, the numbers of vibrations 
of the wire become more frequent directly as its length is 
shortened. Thus, if the wire be shortened 4, 4, 4, or 4, 
the number of its vibrations per second will increase 2, 4, 
3, or 9 times. 

EXPERIMENT 89.—Knowing this law we can readily 
stretch a wire on the sonometer till it gives say the C of 
264 vibrations per second, and then determine the various 
lengths of this wire which when vibrated will give all the 
notes of the gamut. We have seen that the relative num- 
bers of vibrations which give the sounds of the gamut 
are as follows: 


LiPi a OE etl ee aenliage grin” SR Ries Me Case Be ke GaAs Boe 
Relative number of vibrations... 24 27 380 32 36 40 45 48 
Lengths of wire (in centimetres).120 1063 96 90 80 72 64 60 


We have seen that, if the whole length of 120 centi- 
metres of wire gives C, then 60 centimetres must give c of 


_ the octave above, and, as the relative numbers of vibrations 


of G and C are to each other as 86 is to 24, it follows that 
the length of the C-wire must be longer than the G-wire 


1382 SOUND. 


in the ratio of 36 to 24. Hence the proportion 36 : 24 
: : 120: 80 gives 80 centimetres as the length of the G- 
wire. In like manner the lengths of wire which give the 
other sounds of the gamut have been calculated. In the 
third line of the above table we have given these lengths 
in centimetres. Lay off these lengths on the sonometer, 
always measuring from the left-hand bridge toward the 
right, and draw lines across the top of the sonometer 
through these points of division and letter them in order 
D, E, F, G, A, B,c. If you now place the block # (Fig. 
46) successively at these divisions, and vibrate the frac- 
tions of the wire so made, you will obtain in succession 
the notes of. the gamut. | 


EXPERIMENTS WITH THE SONOMETER, GIVING THE HAR- 
MONIC SOUNDS. 


There is another series of sounds called the harmonic 
sounds,in which the relative numbers of the vibrations 
making them are as 1:2:3:4:5:6:7:8:9: 10, ete. 
The law ruling the vibrations of wires and strings teaches - 
us that this series of sounds will be given by the sonome- 
ter if we vibrate its wire after it has been successively 
shortened 4, 1, 4, 4, 4, 4, 4, 4, x, etce., of its: whole 
length. 

EXPERIMENT 90.—Again place the sonometer before 
you, and taking the metric measure divide the length of 
the top between the bridges into 4, 4, 4, 4, 4, 4, 4, 4, + of 
120 centimetres. This is done by measuring in order, 
from the left-hand bridge (Fig. 46) toward the right, 60, 
40, 30, 24, 20, 17.14, 15, 13.33, and 12 centimetres. Draw 
lines through these points of division across the top of the 


EXPERIMENTS WITH THE SONOMETER. 133 


sonometer, and number them in order 4, 4, 4, 4, 4, 4, 
. zo: 

Now place the block /' at each of these lines of divis- 
ion and vibrate the successive fractions of the wire, and 
you will have produced in order the sounds of the har- 
“monic series. 

If we make the whole string vibrate the sound 


Colm 


3 


of 66 vibrations per second, then the harmonic series 
of this C will be as follows. The numbers of vibra- 
tions are written under the names of the notes. The 
latter are given in letters accented to indicate the 
octaves. 


a a eS 


SS SSS 


Ot ees oe er te bh Ten gin Fy 
66 1382 198 264 330 396 462 528 594 660 
ee te ape te A Sy ee frye oe eB oer Ob. = 10) 


_ The lowest sound of a harmonic series is called 
by the names of fundamental, or first harmonic, or 
prime. The other sounds are known as the 2d, 3d, 
4th, etc., harmonic, or as 1st upper partial tone, 2d 
upper partial tone, etc., or as Ist, 2d, 3d, etc., har- 
monic overtones. 

The harmonics of the wire may be obtained in other 


134 ' SOUND. 


ways, making the following series of beautiful experi- 
ments : 


A Vv ne uv’ B 

<<< 

a 
a n Vv n’ ue 

Ae eee 

} 
aw n vw nr v nr oe" 
4. 
Vv Tu w n ar n uw n’ <a 

Y” eircom 

a 
Fie. 47. 


(2), (3), (4), and (5), of Fig. 47, show a wire, A B, which 
has been made to divide itself into 2, 3, 4, and 5 separate 
vibrating parts, lettered v. These vibrating parts, or 
ventres, as they are sometimes called, are separated from 
one another by points marked n, called nodes, where the 
wire is nearly at rest. Adjoining ventres are always vi- 
brating in opposite directions ; that is, while one is going 
up the other will be going down, making a sort of seesaw 
motion around the points 7. 

As 4, 4, 4, and 4, etc., of a wire vibrates 2, 3, 4, 
and 5 times as frequently in a second as the whole 
length of wire, it follows that (2), of Fig. 47, gives the 
2d harmonic, (8) gives the 3d, (4) the 4th, and (5) the 
5th harmonic. 

ExPERIMENT 91.—With a violin-bow the wire may be 
divided into as many as ten vibrating ventres, or seg- 


EXPERIMENTS WITH THE SONOMETER. 135 


ments. Place the tip of the finger or the beard of a quill 
successively over the harmonic division lines on the so- 
nometer, at n’, Fig. 47, and draw the bow across the 
string at v’, and the wire will divide itself into vibrating 
parts whose number will equal the number of the har- 
monic sound given by the wire. 

If little paper riders of this form, ,, be placed on the 
string at the points n’, n, n, n, etc., and v’, v, v, v, etc., 
on vibrating the wire the riders will remain seated at the 
points 7’, n, etc., but those at the points v’, v, etc., will 
be thrown off. 

Soon we shall find these harmonic sounds becoming 
very interesting to us, for they will serve to explain things 
about sounds which, until quite recently, had remained 
unknown. 


PROFESSOR DOLBEAR’S METHOD OF MAKING MELDE’S EX- 
PERIMENTS ON VIBRATING CORDS. 


ExpERIMENT 92.—“To one prong of a small pocket 
tuning-fork tie a piece of silk thread, six or eight inches 
long, and to the other end tie a pin-hook, and hang upon 
it a small weight, say a shirt-button. Project this with a 
lens on a screen. First, with the fork held in a horizontal 
position, vibrate the prongs in a vertical plane. The 
string will divide up into segments, all of which can be 
plainly seen and counted. Second, turn the fork so that 
it vibrates in a horizontal plane. The number of seg- 
ments will be doubled.” 

We have found it preferable to use balls of wax in- 
stead of buttons, so that the precise tension of string re- 
quired in these experiments may be reached by altering 
the size of the suspended wax. It will be found that the 


136 SOUND. . 


number of segments into which the string divides is in- 
versely as the square roots of the weights of the wax 
balls. This fact shows that the frequency of the vibra- 
tions of a string varies inversely as the square root of the 
stretching force applied to it. 


INTENSIDEBS=OF “SOUNDS. 137 
ey, TU UP DOlm Dp = 


gr. ~% § 4 \ tl 
Om WY\VERS PP AS : 
ANN | sagt i fips 
vw, & N 
ies te ie ee ee 
ro 4 if 


CHAPTER XIII. 


ON THE INTENSITIES OF SOUNDS. 


/ EXPERIMENT SHOWING THAT, AS THE SWINGS OF A VI- 
BRATING BODY BECOME LESS, THE SOUND BECOMES 
FEEBLER. 


Your experiments have shown you that the pitch of a 
sound rises with the frequency of the vibrations. You 
no doubt have observed that sounds may be loud or soft 
without regard to their pitch. Thus, just after we 
have vibrated a tuning-fork, its sound is the loudest, 
then it gradually grows feebler and feebler, and slowly 
dies out. 

EXPERIMENT 93.—Let us make an experiment which 
will tell us the cause of this gradual change in the inten- 
sity of its sound. 

Vibrate the fork, as shown in Experiment 25, and very 
slowly draw the smoked glass under the pointed piece of 
foil which is fastened to one of the prongs. As the glass 
slowly moves under the vibrating fork you will observe 
that the sound grows feebler and feebler, and at last it 
dies out. 

Take the glass and examine the trace made by the 
vibrating fork. You see that the lamp-black has been 


138 SOUND. 


scraped from the glass in a triangular-shaped space, as 
shown in Fig. 48. This shows that, as the sound dimin- 


Fie. 48. 


ished in intensity, the extent of the swings of the fork 
grew less and less. 


CO-VIBRATION. 139 


CHAPTER XIV. 
ON CO-VIBRATION. 


EXPERIMENTS WITH TWO TUNING-FORKS. 


EXPERIMENT 94,—Take the two tuning-forks that we 
used in the experiments in interference, and holding one 
upright before you make the other vibrate, and then bring 
the two close together, with the surfaces of their prongs 
opposite each other. One is silent and motionless, the 
other is vibrating. Hold them there for a few seconds, 
and then bring the fork that was silent quickly to the ear, 
and you will discover something quite surprising. It is 
not silent, it is sounding faintly. It has not been touched, 
and yet it is vibrating. Why should a fork begin to vi- 
brate merely because a sounding fork is near it ? 

EXPERIMENT 95.—Get the two wooden boxes or res- 
onators we made for these forks (A-forks) and place 
them on a table with the open ends facing each other, 
and a few inches apart. Hold one of the forks upright 
on one of the boxes, and then, making the other fork 
sound, place it on the other box. It now sounds clear and 
loud. Stop this vibrating fork by touching it with the 
finger, and the other fork will be heard sounding alone. 
This is certainly a most curious matter. That a vibrat- 
ing fork can cause another near it to sound seems im- 


140 SOUND. 


possible, and yet our experiment shows that it is pos- 
sible. / 


EXPERIMENTS ON THE CO-VIBRATION OF TWO WIRES ON 
THE SONOMETER. 


ExPERIMENT 96.—Stretch the two wires on the so- 
nometer (Fig. 46) so that they come in tune with each 
other. If you cannot do this, get some one familiar with 
music to help you, and let him bring the two strings into 
unison. When this is done pull one of the strings at the 
centre and let it go and then watch the other string. At 
first it is at rest and silent, but in an instant it too be- 
gins to quiver and sound. You may repeat this several 
times, and each time you will observe the same thing. 
One string sounding near another causes it to sound also. 

EXPERIMENT 97.—Loosen the second wire slightly 
and put it out of tune with the first, and the experiment 
fails completely. Take another fork, not in tune with 
the one that sounds, and Experiment 95 will also fail. 
Here we are coming on a fact in this matter that may 
help us out. When the two forks are alike, when the two 
strings of the sonometer are in tune, the sounding fork or 
string makes its neighbor sound with it. 

This remarkable fact, that a vibrating body may cause 
another elastic body in tune with it also to vibrate, is called 
co-vibration ; which means, vibrating with (another body). 

The fork (or string, or any body), in vibrating, gives 
to the molecules of the surrounding air the same number 
of pushes and pulls in one second as the silent fork does 
when it vibrates. 

Suppose that the silent fork receives a feeble push from 
the vibrating air which touches it. The prong of the fork 


CO-VIBRATION. 141 


is pressed forward, but through a very minute distance ; 
then it swings back by its own elasticity, but it swings back 
with the air, which now pulls it. Then, on reaching the 
end of this backward swing, it at once gets another push 
from the air, and this push aids it on its forward swing, 
and makes it swing a very little more than it would have 
done if it, had not received this push. Thus the little 
pushes and pulls of the air keep exact time with the tiny 
forward and backward swings of the fork, and, as several 
hundred of these pushes and pulls act,on the fork in a 
second, they soon get it swinging sufficiently to make it 
act- with power enough on the air to give us a sound when 
the other fork is stopped. 

An exact understanding of how these feeble pushes 
and pulls of the air can set into vibration such a stiff and 
heavy body as a steel fork may be rendered clear by the 
following : , 


EXPERIMENT OF SWINGING A HEAVY COAL-SCUTTLE BY 
THE FEEBLE PULLS OF A FINE CAMBRIC THREAD. 


EXPERIMENT 98.—Take a very heavy body, like a 
scuttle full of coal, and suspend it by a stout piece of 
twine. Then tie a piece of the finest cambric thread to 
the handle on the back of the scuttle. When the scuttle 
is hanging motionless give the cambric thread a feeble 
pull, being careful not to pull too hard or you will break 
it. Now you will see, by looking sharply, that you have 
set the scuttle swinging, but through a very small dis- 
tance. Again gently pull the thread when the scuttle is 
swinging toward you, and repeat this pull several times, 
always keeping time with the swing of the scuttle. Now 
the scuttle is swinging through an inch or two, and by 


142 . SOUND. 


keeping up the pulls you may be able to swing it through 
afoot or more. But if your pulls on the thread are not 
in time with the swings of the scuttle you will not be able 
to swing it. 

EXPERIMENT 99.—Now that the scuttle is swinging 
through a foot or so, hold the thread fast so that it can- 
not follow the scuttle. It snaps asunder and the scuttle 
goes on its way, as far as you can see, as though it had 
received no check at all on its speed. This is so because 
the strongest pull you can give through the thread to stop 
the scuttle is only a very small part of the force you have 
already given the scuttle by your many small pulls 
through the thread. 

As the many feeble pulls of the delicate thread at 
length made the scuttle swing with great force, so the 
many feeble pushes and pulls of the delicate air brought 
the fork into a state of vibration powerful enough to make 
all the air in the room tremble. 

This co-vibration may be found wherever two bodies 
in tune are placed near each other. Co-vibration explains 
why the tuning-forks sounded so much louder when placed 
on the resonant boxes. The volume of air inside the box 
is in tune with the fork, and it takes up the vibrations 
sent through the box, and, vibrating with the fork, the 
united vibrations make the sound so much the louder, 
The air in the tumbler and bottles of Experiments 43 and 
63, and the air inclosed in glass tubes, as in Experiments 
78 and 81, also move by co-vibration. It is also by the 
co-vibration of resonant pipes that the feeble notes on the 
lips and reeds of organ-pipes are made full and powerful. 


CHANGES IN PITCH OF A VIBRATING BODY. 143 


CHAPTER XV. 


ON CHANGES IN THE PITCH OF A VIBRATING BODY 
CAUSED BY ITS MOTION. | 


EXPERIMENT IN WHICH THE PITCH OF A WHISTLE IS 
CHANGED BY SWINGING IT ROUND IN A CIRCLE. 


ExperIMENT 100.—Take the piece of rubber tubing 
used in Experiment 382 and fit it over the mouth of the 
whistle used in Experiment 33. Let some one go to the 
end of the room or stand at a distance out-of-doors. Then, 
by the tube, swing the whistle round in a vertical circle, 
and at the same time blow through the tube so that the 
whistle will sound. The observer will see the whistle 
alternately coming toward him and going away from 
him, and with these motions he will hear the pitch of the 
whistle rising and falling. 

In this experiment the sounding body is moving, and 
its movements cause a change in the number of vibrations 
which the ear receives in a given time. When the whistle 
swings toward the observer the sonorous waves are crowd- 
ed together, and they reach the ear in greater number than 
when the whistle is at rest, and the note appears to have © 
a higher pitch. On the other hand, when the whistle 
moves away from the observer, its backward movement 


draws out the sonorous waves, and fewer vibrations are 
7 


144 SOUND. 


given to the ear than when the whistle is at rest. Thus 
we see how the motion of a vibrating body changes the 
pitch of its sound. : 

EXxpPERIMENT 101.—You must notice the same thing 
on the railway, where the sound of the whistle or bell of 
a moving locomotive appears to change in pitch as the en- 
gine draws swiftly near and then passes quickly away 
from us. 


QUALITY OF SOUNDS. 145 


VY CHAPTER XVI. 
ON THE QUALITY OF SOUNDS. 


Wuewn you hear the sound of a violin, flute, clarinet, 
trumpet, piano, or organ, you readily recognize the sound 
of each instrument though it may not be in sight. Some 
one sings or speaks, and another person sings near him or 
after him, and we at once recognize each singer’s or speak- 
er’s voice; and if we are familiar with his voice we can 
give his name, even if we do not happen to see him. This 
leads us to think that there must be some other character- 
istic of sounds besides pitch and intensity. 

The flute, the violin, the clarinet, the singer, may 
each give the same note, and with equal power, yet the 
note of each has a character of its own, a peculiar some- 
thing that distinguishes it from the same note given by 
the other instruments or singers. This we call the quality 
of the sound (sometimes called timbre, or character). 
Let us now make some ; , 


EXPERIMENTS ON THE QUALITY OF SOUNDS. 


The experiments now to be made are of a peculiarly 
fascinating character. They will have for their object 
the discovery of what gives to sounds their various quali- 


146 SOUND. 


ties. These experiments will lead us to the understand- 
ing of some of the laws of music. 

All sounds may be divided into two great divisions. © 
They are either simple sounds or compound sounds. 

EXPERIMENT 102.—A simple sound is one in which 
the ear cannot distinguish two or more sounds differing 
in pitch. Hold one of your vibrating forks over the res- 
onant tumbler, tuned by partly closing its mouth with 
the glass plate, as shown in Experiment 43. You now are 
listening to a simple sound, a sound in which the ear can 
detect only a sound of one pitch. A wide closed organ-pipe 
also gives a simple sound. Allsimple sounds have necssarily 
the same quality, for they differ only in pitch and intensity. 

A compound sound is a sound formed of two or more 
simple sounds, all differing in pitch. Such is the sound 
given by a piano-wire. It may surprise you to learn that 
more than one sound is heard when you strike a piano-key 
which can vibrate only one wire. Yet this is so. 

EXPERIMENT 103.—Strike the c’-key of the piano and 
sound your c’-fork. Though the same note in written 
music stands for each of these sounds, yet your ear at 
once perceives a marked difference in them. Now fix 
your attention on the sound given by the fork alone. Re- 
membering well this sound, strike the c’ of the piano. You 
now recognize that the ce” of the fork is in the sound of 
the piano c’; but after some practice the ear begins to 
- hear other sounds in the piano c’—sounds which are evi- 
dently higher in pitch than the pitch of the fork’s c’. 

The c’ of the fork is certainly the loudest simple sound 
heard in the piano ce’, and it is also the gravest ; there- 
fore the compound sound given by the piano is given in 
written music by the same note which stands for the ¢’ 
of the fork, 


QUALITY OF SOUNDS. 147 


But what are the higher sounds mingled with this c” ? 
I will first answer this question in the most general man- 
ner, then you must make for yourself the experiments 
which will answer it better than my words. 

All compound musical sounds are formed of simple 
sounds, and these simple sounds are the sounds of the har- 
monic series. You have already become acquainted with 
these sounds. You know that the relative numbers of the 
vibrations giving them are as 1:2:3:4:5 : 6, ete. 
The gravest (1) of this series of sounds.is called the fun- 
damental. It is also nearly always the loudest, and the 
compound sound is named after it. This is the sound of 
the c’-fork heard in the ec” of the piano. 

If what I have said is so, then if you strike the C be- 
low the middle C on the piano you will cause other sounds 
to come forth at the same time, sounds which are the har- 
monics of C, and are given by the following notes written 
in the treble stave, and numbered 2, 3, 4, 5, 6, 7, and 8. 
Experiment 104 of the next chapter shows that this is so. 


148 SOUND. 


CHAPTER XVII. 


ON THE ANALYSIS AND SYNTHESIS OF SOUNDS. 


AN EXPERIMENTAL ANALYSIS OF THE COMPOUND SOUNDS 
OF A PIANO. 


ExpreRIMENT 104.—Take your seat in front of the 
keys of the piano, and slowly and steadily press down the 
key of the note c’, marked 2 in the above notation. The 
damper will lift from off the wire, the hammer will ascend, 
touch the wire, and then fall. ‘Thus this wire is free to 
vibrate. Now strike strongly the fundamental note ec, 
marked 1, and, holding it for a few seconds, remove the 
finger. This wire ceases to vibrate, but at once there 
comes to the ear a higher note. It is the sound of the 
free wire of note 2. This experiment shows that the num- 
ber of vibrations which makes the sound of note 2, or ¢’, 
must have been in the sound of note c, or 1, otherwise 
the wire of c¢’ could not have entered into vibration. 
Evidently the wire c' co-vibrated to the simple sound c’ 
contained in the compound sound of the fundamental 
note c, or l. 

Now make similar experiments by depressing in or- 
der the keys of the notes g’, c’, e’, g", c’’’, marked re- 


ANALYSIS AND SYNTHESIS OF SOUNDS. 149 


spectively 3, 4, 5, 6, and 8. You will discover that the 
wire of each of these notes will co-vibrate to the compound 
sound of c, showing that each of these sounds exists in the 
c of the piano. 

Some of these notes will sound out louder or feebler 
than others, showing that they exist with more or less 
force in the compound sound. This fact proves that the 
quality of a sound does not alone depend on the number 
of the simple harmonic sounds which compose it, but also 
on their relative intensities. It can indeed be shown by 
calculation that, if the compound sound be formed of six 
simple harmonic sounds, you can, by giving to each har- 
monic only two different degrees of intensity, form by 
their various combinations upward of 400 different quali- 
ties of sound ; and with four different degrees of intensity 
allowed to each of the six harmonics their combination 
can produce over 8,000 different qualities of sound. Thus 
you see how varied may be the qualities of sounds even 
when they contain the same simple sounds. 

But the same harmonics do not exist in all compound 
sounds. ‘The flute-sounds may contain two or three har- 
-monics. The clarinet-sounds are formed of the funda- 
mental, the 3d, the 5th, and the 7th. The violin-sounds 
contain all the harmonics up to the 7th, and often to the 
10th. The composition of piano-sounds varies with their 
pitch. The deeper tones are rich, but the higher are poor, 
in harmonics. In the lower octaves the 3d harmonics are 
often as loud as the fundamental harmonic, and the 2d 
harmonic is often even louder. Reed organ-pipes are very 
rich in harmonics, often extending as high as the 20th, 
and readily detected by a practised ear, which can pick 
one after another out of the compound sound, almost. to 
the exclusion of hearing the rest. The human voice is 


150 SOUND. 


rich in harmonics, and varies much in quality, as we all 
know from listening to different singers. The quality 
also varies with the pitch of the notes sung, as will be 
shown by experiments with Kénig’s vibrating flames. 
(See Experiment 112, and following.) 


EXPERIMENTS IN WHICH WE MAKE COMPOUND SOUNDS 
OF DIFFERENT QUALITIES BY COMBINING VARIOUS SIM- 
PLE SOUNDS. 


EXPERIMENT 105.— The jflute-sound may be made by 
combining a simple sound with its octave. The following 
experiment produces it very well: You found that a col- 
umn of air, in a tube, just one-fourth of the length of the 
sonorous wave given by a fork, will strengthen by its co- 
vibration the sound of the fork. If you make the column 
of air in the tube only one-eighth of the length of the 
wave it will resound to the octave of the fork, for columns 
of air in tubes (as shown on page 122) follow the same law 
of vibration as stretched wires and strings ; that is, their 
vibrations increase in frequency directly as the air-column 
is shortened. | 

The de»th of air-column which resounds to the A-fork 
is 7% inches (19.47 centimetres). Push the cork up the 
glass tube (see Experiment 78) till you have an air-column 
one-half of this length, or 3.83 inches (9.73 centimetres). 
Now vibrate the fork and bring it over the mouth of the 
tube. A clear flute-like sound comes forth. It is formed 
of the A-note of the fork mingled with its octave given 
by the resonant tube. By properly varying the distance 
of the fork from the tube, and both from the ear, you will 
after a few trials obtain a sound which you can barely 
distinguish from that of a flute. 


ANALYSIS AND SYNTHESIS OF SOUNDS. 151 


EXPERIMENT 106.—TZhe sounds of the human voice 
can be formed out of its simple sounds by using the co- 
vibration of the strings of the piano. 

Lift the top of the piano. Strike a key and then sing 
it till you are sure that you have its pitch. Press down 
the pedal so that the dampers are lifted from all of the 
wires, then lean over the wires and clearly and steadily 
sing the note. Stop and listen. The piano answers back, 
and the sound of your voice is heard as though coming 
from a distance. Each string which is in tune to a har- 
monic in your voice co-vibrates with that harmonic, and 
all of the harmonics of your voice are thus sounded by 
the strings of the piano. The combination of all these co- 
vibrations builds up the quality of your voice and echoes 
it back to you. 

EXPERIMENT 107.—If you now sing again the 
same note, and press down one after the other the 
keys of its harmonics, as we did in our other experi- 
ment with the piano, you may find out what harmonics 
compose your voice, and get some idea of their rela- 
tive strengths. 

EXPERIMENT 108.—If a cornet, a clarinet, our little 
toy trumpet, or other instrument, be sounded over the 
freed strings of the piano, their sounds will be analyzed 
by the co-vibrations of these strings. Then the sounds 
of the strings melt into one compound sound, which is 
the reproduction of the sound of the instrument which set 
the strings in motion. _ 

Thus we see that every musical sound, whether from 
voice or instrument, is formed of a fundamental combined 
with a certain number of harmonics. 

Your unpractised ear may not always be able to pick 
them one by one out of the tangle of sound. Yet there 


152 SOUND. 


they exist, giving those delicate and ethereal qualities 
which characterize the various sounds of Nature and of 
music. 


HOW THE EAR ANALYZES A. COMPOUND SOUND INTO ITS 
SIMPLE SOUNDS. 


The experiments with the piano serve to explain the 
wonderful power of the ear in analyzing compound sounds. 
In the cochlea (snail-shell, C of Fig. 4) of the ear are sup- 
posed to exist co-vibrating fibres which are tuned to sim- 
ple sounds extending over several octaves. To each tuned 
tibre is fastened a fine filament of the auditory nerve. A 
simple sound is only given by a pendular vibration. A 
compound sound is a sensation made by several pendular 
vibrations of various frequencies entering the ear together.: 
If one pendular vibration enters the ear it vibrates the 
nerve-filament fastened to the fibre which is tuned to 
this pendular vibration, and we have the sensation of a 
simple sound. 

But when a compound vibration, made up of several 
simple pendular vibrations, enters the ear, it acts on sev- 
eral tuned fibres, exactly as our voice, or the sounds of the 
cornet or trumpet,.acted on several piano-strings. Each 
fibre. in the ear enters into vibration with that pendular 
vibration in the compound sound with which it is in tune. 
Thus the nerve-filaments are shaken which are fastened 
to fibres in the ear tuned to the simple sounds in the 
compound sound, and the sensation of the latter is thus 
analyzed into its Simple sound sensations. What we 
have just said suggests at once the question: What sort 
of motion has a molecule of air when it is acted on at 
the same time by several epansales vibrations? ‘This is 
answered by 


ANALYSIS AND SYNTHESIS OF SOUNDS. 153 


AN EXPERIMENT WHICH SHOWS THE MOTION OF A MOLE- 
CULE OF AIR, OR OF A POINT ON THE DRUM-SKIN OF 
THE EAR, WHEN THESE ARE ACTED ON BY THE COM- 
BINED PENDULAR VIBRATIONS OF THE FIRST SIX HAR- 
MONICS. 


We have seen, in Experiment 11, that the pendu- 
lar motion may be obtained by sliding a card, with 
a slit in it, over the sinusoidal trace of a vibrating 
rod. Imagine a similar trace made by a point whose 


Fie. 49. 


motion is formed of the combined vibratory motions of 
the first six harmonics. Such is the trace drawn on the 
line ed of Fig. 49. 

ExpPERIMENT 109.—If we slide, in the direction cd, a 
card with a slit in it over this trace, you will see in the 
slit the same vibratory motion, only much slower, that a 


154 SOUND. 


point of the drum-skin of the ear has when we hear a 
compound sound (like that of the piano-wire) which con- 
tains the first six harmonics. The student of course re- 
-members that the direction of the length of the slit is in 
the direction in which the sonorous vibration is traveling 
through the air. 

-The curve on cd I obtained as follows : I drew on the 
line a6 the six sinusoids, having their lengths as 1:2 :3 : 
4 :5:6. Another line, ¢ d, was drawn below and parallel 
to a6, and then 500 equidistant lines, perpendicular to ad, 
were drawn through the curves on ab and extended below 
the line cd. On each of these vertical lines I got the 
algebraic sum (calling the distances above a6 + and those 
below cd —) of the distances of the curves above or below 
ed, and ‘then transferred this sum to the corresponding 
vertical line passing through ed. Through the points thus 
found, above and below cd, I drew the curve which you 
see on cd. | 

EXPERIMENT 110.—This curious compound sonorous 
motion is best exhibited as follows : On a piece of card- 
board draw a circle, and in one quadrant of this circle 
draw 500 equidistant radii. Make the length of these 
radii vary with the corresponding distances of the curve 
(Fig. 49) above and below the line ed. Join the ends of 
these radii with a curve. By repeating this curve four 
times on the cardboard you will have made the curve con- 
tinuous, as is shown in Fig. 50. Now cut this curved fig- 
ure out of the cardboard, and thus form a templet. Place 
this, centred, on a glass disk of a foot in diameter, coy- 
ered with opaque black varnish. With the separated 
points of a pair of spring dividers scribe around the edge 
of the templet, and thus remove the varnish in a sinuous 
band, as shown in Fig. 50. 


ANALYSIS AND SYNTHESIS OF SOUNDS. 155 


The glass disk is now mounted on the rotator, and 
placed between the heliostat and a plano-convex lens, as 
shown on page 79 in our book on “Light” of this series. 
A magnified image of that portion of the curve which is in 
front of the heliostat is thus obtained on a screen. A 


Fie. 50. 


piece of cardboard, having a narrow slit cut in it, is now 
placed close to the disk and in the direction of its radius. 
Revolving the disk you will have on the screen a vibra- 
tory motion like that which a molecule of air, or a point 
on the drum-skin of ‘the ear, has when these are acted on 


156 _ SOUND. 


by the combined pendular vibrations of the first six har- 
monics of a musical note. ; 

On slowly rotating the disk one can readily follow the 
compound vibratory motion of the spot of light on the 
screen. On a rapid revolution of the disk the spot ap- 
pears lengthened into a luminous band, but this band is 
not equally illuminated. It has six distinct bright spots 
in it, beautifully showing the six bends in the curve on 
the disk. 

EXPERIMENT 111.—The student, however, need not 
go to the expense of buying the glass disk. He is able, 
no doubt, to copy on a cardboard the curve, about three 
times as large as Fig. 50, and then, turning it on the ro- 
tator before a slit in a card, he may study at his leisure 
this curious motion. He can even get this motion, directly 
from the figure in his book by sticking a pin in the cen- 
tre of Fig. 50, and about this revolving a card with a 
fine slit in it. 


( EXPERIMENTS BY WHICH COMPOUND SOUNDS ARE ANA- 
LYZED BY VIEWING IN A ROTATING MIRROR THE VI- 
BRATIONS OF KONIG’S MANOMETRIC FLAMES. 


Take a piece of pine board, A, Fig. 51, 1 inch (25 mil- 
limetres) thick, 14 inch (38 millimetres) wide, and 9 inches 
(22.8 centimetres) long. One inch from its top bore with 
an inch centre-bit a shallow hole 4 inch deep. Bore a like 
shallow hole in the block B, pinche is 3 inch thick, 14 inch 
wide, and 2 inches (51 millimetres) ae Place a inh 
centre-bit in the centre of the shallow hole in A and bore 
with it a hole through the wood. Into this fit a glass or 
metal tube, as shown at & Bore a ;*,-inch (5 millimetres) 
hole obliquely into the shallow hole in B, and into this fit 


157 


ANALYSIS AND SYNTHESIS OF SOUNDS. 


the glass tube C. Then bore another 3;-inch hole directly 


into the shallow hole in B. Put a glass tube in a 


gas or 


hot at a place about two inches 


- Spirit flame and heat it red 


Fig. 51. 


from itsend. Then draw the tube out at this place into 


a narrow neck. Make a cut with the edge of a file across 
this narrow neck, and the tube will readily snap asunder 


158 SOUND. 


at this mark. Then heat a place on the tube in a flame, 
and here bend it into a right angle, as shown at D, Fig. 
51. Now fit this tube into the hole just made, as shown 
at D. These tubes may be firmly and tightly fitted by 
wrapping their ends with paper coated with glue before 
they are forced into their holes. 

Get a small piece of the thinnest sheet rubber you can 
find, or a piece of thin linen paper, and, having rubbed 
glue on the board A around the shallow hole, stretch the 
thin rubber, or paper, over this hole and glue it there. 
Then rub glue on the block , and place the shallow 
hole in this block directly over the shallow hole in A, 
and fasten B to A by wrapping twine around these blocks. 
Thus you will have made a little box divided into two com- 
partments by a partition of thinrubber. Fasten the rod A 
to the side of a small board, so that it may stand upright. 

Attach a piece of large-sized rubber tube to the glass 
tube , and into the other end of the tube stick a cone, 
made by rolling up a piece of cardboard so as to form a 
cone 8 inches long and with a mouth 2 inches (51 milli- 
metres) in diameter. 

Now get a piece of wood 1 foot long, 4 inches 
wide, and + inch thick. Out of this cut the square, 
with the two rods projecting from it, as shown at 
M. ‘The lower of these rods is short, the one above the 
square is long. Cut the end of the shorter rod to a blunt 
point, and with this point make a very shallow pit in the 
piece of flat wood Jt for the rod and square to twirl in. 
Glue the piece of wood £ on the end of a brick, Z. Get 
two pieces of thin silvered glass, each 4 inches square, 
and, placing one on each side of the square J/, fasten them 
there by. winding twine around the top and bottom borders 
of the mirrors. 


ANALYSIS AND SYNTHESIS OF SOUNDS. 159 


EXPERIMENT 112.—Through a rubber tube lead gas to 
C. It will go into the left-hand partition of the box and 
will come out at 7} where you will light it. Now place 
the mirror-rod. in the shallow pit in 4, and hold the mirror 
upright so that you may see the flame /’ reflected from its 
centre. 

Hold the rod upright and twirl it slowly between the 
thumb and forefinger, which should point downward and 
not horizontally, as shown in the figure. The flame appears 
in the mirror drawn out into a band of light with a smooth 
-top-border. While twirling the mirror put the cone to 
your mouth and sing into it. The sonorous vibrations 
enter the side A of the box, and, striking on the thin rub- 
ber, force this in and out. When it goes in, a puff of gas 
is driven out of the other partition, .B, of the box, and the 
flame # jumps up. When the sheet of rubber vibrates 
outward, it sucks the gas into the box B, and the flame 1’ 
jumps down. Therefore, on singing into the funnel, you 
will see in the mirror the smooth top-border of the lumi- 
nous band broken up into little tongues or teeth of flame, 
each tooth standing for one vibration of the voice on the 
rubber partition. 

Place a lamp-chimney around the flame, should the 
wind from the twirling mirror agitate it, and be careful 
not to have the flame too high. . 

EXPERIMENT 113.—Another way of showing the vi- 
brations of the flame is to burn the jet of gas at the end 
of a glass tube stuck into the end of a rubber tube attached 
to # Now sling the tube round in a vertical circle, and 
you have an unbroken luminous ring; but as soon as you 
sing into the cone this ring breaks up into a circle of beads 
of light, or sometimes changes into a wreath of beautiful 
little luminous flowers, like forget-me-nots. To make 


160 SOUND. 


this experiment, you will be obliged to have a tube with 
a larger opening than that at / 

This instrument will afford you many an hour of in- 
struction and amusement. We have only space to show 
you a few experiments. Others will suggest themselves 
whenever you use it. 

ExprermMENT 114,—Sing into the funnel the sound of 
00 asin pool. After a few trials you will get a pure sim- 
ple sound, and the flame will appear as in Fig. 52. Some 
voices get this figure more readily by singing E. 

EXPERIMENT 115,—Twirling the mirror with the same 
velocity, gradually lower the pitch of the oo sound till 
your voice falls to its lower octave, when the flame will 
appear as in Fig. 53, with half the number of teeth in Fig. 
52, because the lower octave of a sound is given by half 
the number of vibrations. 

EXPERIMENT 116.—Sing the vowel sound o on the note 


and you will see Fig. 54 in the mirror. This evidently is 
not the figure that would have been made by a simple 
vibration. It shows that this o sound is compound, and 
formed of two simple sounds, one the octave of the other: 
The larger teeth are made by every alternate vibration 
of the higher simple sound acting with a vibration of the 
lower, and thus making the flame jump higher by their 
combined action on the membrane. 

ExpPERIMENT 117.—Fig. 55 appears on the mirror when 
we sing the English vowel a on the note f. 

ExpERrIMENT 118.—Fig. 56 appears on the mirror when 
we sing the English vowel a on the note c. 


ANALYSIS AND SYNTHESIS OF SOUNDS. 161 


Examine attentively Fig. 55. This shows that the 
English vowel a sung on f is made up of two combined 


Figs. 52, 58, 54, 55, 56. 


simple vibrations. One of these alone would make the 
long tongues of flame, but with this simple vibration exists 
another of three times its frequency; that is, the vibration 


162 SOUND. 


of greater frequency is the 3d harmonic of the slower. 
As the slower vibration, making the long tongues of flame, 
is f, the higher must be c” of the second octave above f. 
Each third vibration of this higher harmonic coincides 
with each vibration of f; hence each third tongue of flame 
is higher than the others. 

ExpERIMENT 119.—In like manner the student must 
analyze Fig. 56 into its simple sonorous elements. ‘Then 
he should, with the vibrating flame, examine the peculiari- 
ties of the various voices of his friends, and make neat 
and accurate drawings of the flames corresponding to 
them, so that he may analyze them at his leisure. 

EXPERIMENT 120.—Blow your toy trumpet into the 
paper cone gently, and then strongly, and observe that 
the sound given by the trumpet is a complex one. Try 
if you cannot get a flame somewhat like the trumpet gives 
by singing ah, through your nose, into the cone. 

The student will soon find that different persons, in 
singing the same note, as nearly alike as they can, will pro- 
duce flames of very different forms. This is because the 
voices differ in the number and relative intensities of the 
simple sounds which form them. 

Another cause of the different forms of flame obtained 
by different experimenters is due to the fact that they have 
used different lengths of tube leading from the cone to the 
membrane. 

EXPERIMENT 121.—The fact can readily be proved 
by singing the same compound sound through different 
lengths of tube leading from the cone G to the membrane. 


ANALYSIS AND SYNTHESIS OF SOUNDS. 163 


TERQUEM’S EXPERIMENT, IN WHICH KONIG’S FLAME IS USED 
INSTEAD OF THE EAR (AS IN EXPERIMENTS 68, 69, AND 70), 
AND THUS. THE MOTIONS OF A VIBRATING DISK ARE 
MADE VISIBLE. 


The method of analyzing the motions of a vibrating 
plate (as described in Experiments 68, 69, and 70), with 
the paper cone and tube applied to the ear, which has 
been used by us for a long time, has quite recently been 
adapted to M. Konig’s flame by Professor Terquem, of 
Lille, who has thus made these motions visible to the 
student, and has given us a charming experiment. 

ExpEeRIMENT 122,—If the rubber tube used in con- 
_ nection with the cone in Experiments 68, 69, and 70, is 
attached to the tube # of Fig. 51, instead of being placed 
in the ear, then Konig’s flame will remain at rest when the 
cone is in position No. 1 of Experiment 68, or in position 
No. 3 of Experiment 70. In these positions of the cone 
you found that no sound was heard. But, when the 
mouth of the cone is placed in position No. 2 of Experi- 
ment 69, the flame becomes deeply serrated ; and you 
found in Experiment 69 that in this position an intense 
sound was heard. 


164 HOW WE SPEAK. 


CHAPTER XVIII 


ON HOW WE SPEAK, AND ON THE TALKING MACHINES 
OF FABER AND EDISON. 


HOW WE SPEAK. 


Tue little musical instrument with which we sing and 
speak is formed of two flexible membranes stretched side 
by side across a short tubular box placed on the top of the 
windpipe. This box is made of plates of cartilage, mov- 
able on each other, and bound together with muscles and 
membranes. : 

The top of the windpipe is’ formed of a large ring of 
cartilage, called the cricoid (ring-shaped) cartilage. Joint- 
ed to this is a broad plate of gristle, called the thyroid 
(shield-shaped) cartilage. This cartilage is bent into the 
shape of a V. The legs of this V straddle the cricoid 
and are jointed to its outer sides. The peak of the V 
stands up and points toward the front of your throat. 
You can feel it, as it is the “ Adam’s apple.” On the back 
of the upper edge of the cricoid ring are jointed two 
small pointed cartilages, known as the arytenoid (funnel- 
shaped) cartilages. Stretching from these to the inner 
sides of the legs of the V of the thyroid are two mem- 
branes, one to each leg. These are the vocal chords. 

When the point of the thyroid is not pulled down, 
these membranes are lax, and the breath from the wind-’ 


SOUND. 165 


pipe passes freely between them and does not make them 
vibrate. (See B of Fig. 57.) 


Fig. 57. 


Figs. A and B.—Views of the human larynx from above as actually seen by the aid 
o1 jhe instrument called the laryngoscope. 

Fig. A.—In the condition when voice is being produced. 

Fig. B.—At rest, when no voice is produced. 

é. Epiglottis (foreshortened), . 

ev. The vocal cords. 

evs, The so-called false vocal cords, folds of mucous membrane lying above the 
real vocal cords. 

a. Elevation caused by the arytenoid cartilages. 

8, w. Elevations caused by small cartilages connected with the arytenoids. 

¢. Root of the tongue. 


But when the peak of the thyroid is pulled down by 
its muscles the vocal cords are stretched. At the same 
time the arytenoid cartilages move nearer each other, and 
the thin, sharply cut edges of the vocal chords are brought 
parallel and quite close to each other, as is shown in A of 
Fig. 57. If the air is now forced through this narrow 
slit (called the glottis), the vocal chords vibrate just like 
the tongue in our toy trumpet, or like the reed in any 
reed-pipe. <A puff of air passes between them ; they sep- 
arate; immediately afterward they come close together 
and the current of air is stopped. They again open, 
another puff goes into the cavity of the mouth, and then 
they close together again. Thus the glottis opens and 
closes with a frequency depending on the degree of stretch 
on the vocal chords. 


166 HOW WE SPEAK. 


Our experiments with Kénig’s flame have shown how 
composite are the sounds of the human voice. The quality 
of a voice depends on the number and relative intensities 
of the simple sounds which build it up. 

SPEECH is voice modified and modulated by the move- 
ments of the parts of the cavity of the mouth, of the 
tongue and lips. 

The oral cavity is made larger or smaller, longer or 
shorter, and thus, resounding to some lower or higher har- 
monic of the voice, makes the others feebly heard. 

EXPERIMENT 123.—If you form your speaking organs 
to say o, and then take your vibrating A-fork and hold it 
before your lips, you will hear the cavity of the mouth re- 
sounding to this sound. On changing the vocal organs to 
say e the resonance ceases. 

All the vowel sounds are formed by a steady voice 
modified by the resonance of the different sizes and shapes 
given to the oral cavity. 

The consonants are made by obstructions placed at the 
beginning or end of the oral sounds, by the movements of 
the tongue and lips; but, as this is a book of experiments, 
I leave you to inform yourself by experiments as to these 
matters. 


a 


EXPERIMENTS IN WHICH A TOY TRUMPET TALKS AND A 
SPEAKING MACHINE IS. MADE. 


Exrrerment 124.—Sing ah, and while doing so 
quickly open and shut your lips twice. These two sud- 
den obstructions to the sound have made you say mama. 
If you will observe attentively the motion of your mouth 
you will see that for the last syllable of mama you open 


SOUND. 167 


your mouth wider and keep it open longer than for the 
first syllable. 

EXPERIMENT 125.—This is all we have to know to 
make our toy trumpet talk. You already have seen that 
its sounds, like those of the human voice, are made by 
puffs of air. These pass the reed every time it goes above 
or below the oblong hole in the plate in which it vibrates. 
Your experiments with Kénig’s flame have told you that 
the sounds of the voice and trumpet are similar—that 
both are highly composite. . 


Fig. 58. 


Let, then, the vibrating reed in the trumpet stand for 
your vocal chords. To get a resonant cavity like the mouth, 
make one between your two hands, as shown in A of Fig. 
58. The funnel of the trumpet is placed inside this cavity, 
with the tube coming out in the crotch between the thumb 
and forefinger.. The lips we will form of the fingers of 
one hand. By raising these together, more or less, from 
_the other hand we can make a larger or smaller open- 
ing into the cavity between the palms of the hands, and 
thus get OMe 


168 HOW WE SPEAK. 


Now blow into the trumpet as though you were speak- 
ing mama into it, so that you may make it sound twice, 
each sound lasting just as long as the sounds in ma and 
mi. While making the first sound, raise the fingers as 
high as is shown in A ; while making the second, raise 
them as high as is shown in 6. The trumpet talks and 
says mama quite plainly. 

EXPERIMENT 126,—Let us make a talking machine. 
Get an orange with a thick skin and cut it in halves. 
With a sharp dinner-knife cut and scrape out its soft in- 
side. You have thus made two hemispherical cups. Cut 
a small semicircle out of the edge of each cup. Place 
these over each other, and you have a hole for the tube 
of the trumpet to go out of the orange. Now sew the 
two cups together, except a length directly opposite the 
trumpet, for here are the lips. A peanut makes a good 
enough nose for a baby, and black beans make “ perfectly 
lovely” eyes. Take the baby’s cap and place it on the 
orange, and try if you can make it say 


en 


SOUND. 169 


FABER’S TALKING MACHINE. 


These simple experiments show the principles followed 
in the construction of the celebrated talking machine of 
Faber of Vienna. A vibrating ivory reed, of variable 
pitch, forms its vocal chords. There is an oral cavity 
whose size and shape can be rapidly changed by depress- 
ing the keys on a key-board. Rubber tongue and lips 
make the consonants. A little windmill turning in its 
throat rolls the 7, and a tube is attached to its nose 
when it speaks French. This is the anatomy of this really 
wonderful piece of mechanism. 


EDISON’S TALKING PHONOGRAPH. 


From the above description it is seen that Faber 
worked at the source of articulate sounds, and built up 


an artificial organ of speech, whose parts, as nearly as 


possible, perform the same functions as corresponding or- 
gans in our vocal apparatus. Faber attacked the problem 
on its physiological side. Quite differently worked Mr. 


170 TALKING MACHINES. 


Edison. He attacked the problem, not at the source of 
origin of the vibrations which make articulate speech, 
but, considering the vibrations as already made, it matters 
not how, he makes these vibrations impress themselves on 
a sheet of metallic foil, and then reproduces from these 
impressions the sonorous vibrations which made them. 

Faber solved the problem of making a machine speak 
by obtaining the mechanical causes of the vibrations 
making voice and speech; Edison solved it by obtain- 
ing the mechanical effects of these vibrations. Faber re- 
produced the movements of our vocal organs ; Edison re- 
produced the motions which the drum-skin of the ear 
has when this organ is acted on by the vibrations caused 
by the movements of the vocal organs. 

Figs. 60 and 61 will render intelligible the construc- 
tion of Mr. Edison’s machine. <A cylinder, Z; turns on 
an axle which passes through the two standards A and 
B. On one end of this axle is the crank D,; on the 
other, the heavy fly-wheel # The portion of this axle 
to the right of the cylinder has a screw-thread cut on 
it which, working in a nut in A, causes the cylinder to 
move laterally when the crank is turned. On the sur- 
face of the cylinder is scored the same thread as on its 
axle. At A (shown in $ scale in Fig. 61) is a plate of 
iron about ;4, inch thick. This plate can be moved 
toward and from the cylinder by pushing in or pulling 
out the lever HG, which turns in a horizontal plane 
around the pin J. 

The under surface of this thin iron plate (A, Fig. 61) 
presses against short pieces of rubber tubing, XY and_X, 
which lie between the plate and a spring attached to Z 
The end of this spring carries a rounded steel point, P, 
which, when brought up to the cylinder by the motion of 


SOUND. 171 


the handle 7, enters slightly between the threads scored 
on the cylinder C. The distance of this point, P, from 
the cylinder is regulated by a set-screw, S, against which 
abuts the lever H G. Over the iron plate A is a disk of 


| 
{ \ 


UY { 
@ 4 \ 
| mS = 
HN 
Hi 

TTT TTT T= > 


Fig. 61. 


vuleanite, B B, with a hole in its centre. The under 
side of this disk nearly touches the plate A. Its upper 
surface is cut into a shallow, funnel-shaped cavity lead- 
ing to the opening in its centre. 


172 TALKING MACHINES. 


To operate this machine we first neatly coat the cylin- 
der with a sheet of foil; then we bring the point P to 
bear against this foil, so that, on turning the cylinder, it 
makes a depressed line or furrow where the foil covers 
the space between the threads cut on the surface of the 
cylinder. The mouth is now placed close to the open- 
ing in the vulcanite disk B Bb, and the metal plate is 
talked to, while the cylinder is revolved with a uniform 
motion. 

The thin iron plate A vibrates to the voice, and the 
point P indents the foil, impressing in it the varying num- 
bers, amplitudes, and durations of these vibrations. If the 
vibrations given to the plate A are those of simple sounds, 
then they are of a uniform regular character, and the 
point P indents regular undulating depressions in the foil. 
If the vibrations are those causing complex and irregular 
sounds (like those of the voice in speaking), then simi- 
larly the depressions made in the foil are complex (like 
the curve of Fig. 49) and irregular. Thus the yielding 
and inelastic foil receives and retains the mechanical im- 
pressions of these vibrations with all of their minute and 
subtile characteristics. } | 

Our experiment No, 121 has, however, taught us that 
the forms of these impressions will change with every 
change of distance of the place of origin of the com- 
pound sound from the vibrating plate A, even when at 
these various distances the compound sonorous vibrations 
fall on the plate with precisely the same intensity. Hence 
the futility of attempting to read sound-writings. 

The permanent impressions of the vibrations of the 
voice are now made. It remains to show how the opera- 
tion just described may be reversed, and thus to obtain - 
Jrom these impressions the aérial vibrations which made 


SOUND. : 173 


them. Nothing is simpler. The plate A, with its point P, 
is moved away from the cylinder by pulling toward you 
the lever H G. Then the motion of the cylinder is re- 
versed till you have brought opposite to the point P the 
beginning of the series of impressions which it has made 
on the foil. Now bring the point up to the cylinder ; 
place against the vulcanite plate B £6 a large cone of 
paper or of tin to reénforce the sounds, and then steadily 
turn the crank J). 'The elevations and depressions which 
have been made by the point P now’ pass under this 
point, and in doing so they cause it and the thin iron 
plate to make over again the precise vibrations which 
animated them when they made these impressions under 
the action of the voice. The consequence of this is, 
that the iron plate gives out the vibrations which pre- 
viously fell upon it, and 7 talks back to you what you 
said to it. 


174 TWARMONY AND DISCORD. 


CHAPTER XIX. 


ON HARMONY AND DISCORD. A-SHORT EXPLANA- 
TION OF WHY SOME NOTES, WHEN SOUNDED TO- 
GETHER, CAUSH AGREEABLE AND OTHERS DISA- 
GREHEABLE SENSATIONS. 


Ir, toward sunset, you walk on the shady side of a 
picket-fence, flashes of light will enter your eye every time 
you come to an opening between the pales. These flashes, 
coming slowly one after the other, cause a very disagree- 
able sensation in the eye. Similarly, if flashes or pulses 
of sound enter the ear, they cause a disagreeable sensa- 
tion. Such pulses enter the ear when we listen to two 
sounding organ-pipes, two forks, or two wires on the so- 
nometer which are slightly out of tune with each other. 
As you already know (see Experiment 71), these flashes 
or pulses of sound are called beats. You also know that 
the number of these beats made in a second is equal to 
the difference in the numbers of vibrations made in one 
second by the two sounding bodies. Thus, if one sound- 
ing body makes 500 and the other 507 vibrations in a 
second, then 7 beats per second will be heard. 

EXPERIMENT 127.—With your toy trumpet and the 
disk used in Rood’s experiment in the reflection of sound, 
Fig. 42, you can make an excellent experiment, showing 
the effects of beats on your ear. Sound the trumpet, and 


SOUND. 1%5 


gradually increase the velocity of the turning disk. At 
first the beats of sound so caused may be separately dis- 
tinguished by the ear, and, though not pleasant in their 
effect, yet they can be endured. As the frequency of the 
beats increases, the harshness of the sensation becomes 
greater and greater, until the effect on the ear becomes 
actually painful. 

But, if the flashes of ight or beats of sound aceeed 
one another so rapidly that the sensation of one flash or 
beat remains till the next arrives, you will have continu- 
ous sensations that are not unpleasant. In other words, 
continuous sensations are pleasant, but discontinuous or 
broken sensations are disagreeable. 

If two sonorous vibrations reach the ear together and 
make a disagreeable sensation, then we may be sure that 
the Wi irerante in the numbers of their vibrations gives_a 
number of beats per second which do not follow one an- 
other with sufficient rapidity to blend into a smooth, un- 
broken sensation. In other words, these beats are so few 
in a second that the sensation of one disappears before the 
next arrives, and so discord is the sensation ; but, if the 
frequency of the beats be sufficiently increased, the sensa- 
tion of one remains till the next arrives, and the sensation 
is continuous, and we say that the two sounds are in 
harmony. : 

Therefore it at once appears that, if we only can find 
out the number of beats required in a second to blend 
sounds from different parts of. the musical scale, we shall 
be able to state beforehand what notes when sounded 
together will make harmony and what notes will make 
discord. 

By many experiments I have found the number of 
beats per second that two sounds must make to be in har- 


176 HARMONY AND DISCORD. 


mony. In the following table a few of the results of 
my experiments are given : 


Vv B or 


N 

C 64 16 as = -0625 sec. 
c 128 26 zy = .0384 “ 
e' 256 44 jy = 0212 « 
g 384 60 as = 0166 “ 
c" 512 48 de = .0128 “ 
e” 640 90 oy —- 201 lee 
g" 768 109 sig = 0091 “ 
e” 1024 135 sis = 0074 


Column N gives the names of the notes given by the 
vibrations per second in Column V. The c’ in this series is 
that used by physicists generally, and gives 256 vibrations. 
In Column B is given the smallest number of beats per 
second which the corresponding sound must make with 
another in order that the two may be in harmony, or, 
as it is generally stated, may make with the other the 
nearest consonant interval. If 47 beats per second of c’, 
for example, blend, then the sensation of each of these 
beats remains on the ear 7; of a second. In Column D 
are given these durations in fractions of a second. As 
these fractions are the lengths of time that the sensation 
of sound lingers in the ear after the vibrations of the 
air near the drum-skin of the ear have ceased, they are 
very properly called the durations of the residual sono- 
rous sensations. 

You observe in the table that this duration becomes 
shorter as the pitch of the sound rises. Thus, while the 
residual sensation of C is 7; of a second, that of c’”’ is 
only +4;. 

Let us use the knowledge thus acquired by making it 
aid us in a few calculations and experiments. The table 


SOUND. 177 


shows that if ce’ is sounded with a note which makes with 
it 47 beats in a second, then these beats will fuse into one 
smooth, continuous sensation, and the notes must be in 
harmony. What is this note? It is found in this man- 
ner: c’ is made by 256 vibrations per second, and the 
note which will make just 47 beats with it in a second 
must make 256+ 47 or 303 vibrations in a second. This 
number of vibrations makes a sound a little lower in pitch. 
than be’. ‘This is the minor third of c’. 

ExpERIMENT 128,—Now let one sing c’ while another 
sings be’, and you will find that these sounds form an in- 
terval which is just within the range of harmony. 

EXPERIMENT 129.—Sing c’ and e’, then c’ and g”, and 
you will have yet more pleasant and smooth sensations. 

ExrErRmMENT 130.—But if one sings c’ while another 
sings d’ you have decided discord, an unpleasant rasping 
sensation in the ears. The reason of this is at once ap- 
parent : c’ makes 256 while d’ makes 288 vibrations in a 
second, and 288 less 256 gives 32 as the number of beats 
made in a second; but the table shows that 47 are needed 
in a second so that they may follow each other quick 
enough to blend. 

Making similar calculations throughout five octaves, 
we have found the nearest consonant intervals for the c of 
each octave from C toc’. These are here given. It will 
be observed that this interval contracts as we ascend the 
musical scale—a fact which has been well established. 


The nearest consonant interval of C is its major third. 


i 5 re “¢ “ minor third. 

* “ ¢’ “ minor third, less 14 semitone. 
‘ 79 6c (79 tt ce 6c 66 “ce 

ce ¢ c 7A 

iT “ cc cc a“ el” cc second. 


wo é - “ civ “ second, less 14 semitone. 


178 HARMONY AND DISCORD. 


Our experiments in sound have led us into music. We 
find that fundamental facts and laws of harmony may be 
explained by physiological laws—by rules according to 
which our sensations act. Music is the sequence and con- 
course of sounds made in obedience to these laws. The 
explanation of many of these may be beyond our power ; 
for the connection existing between esthetic and moral 
feelings and sensations which cause them remains be- 
hind a veil. But it may be imagined that distant ages 
may bring forth man so highly organized that he may 
find his pleasure and pastime in 


“ Untwisting all the chains that tie 
The hidden soul of barmony.” 


- THE END, 


List of Apparatus used in the Experiments on Light 
and Sound, with the prices, as supplied by Samuel 
Hawkridge, successor to George Wale § Co., Ho- 
boken, New Jersey. 


ibahCalahst 
Pipirsaktee ee ee ie cera aha ate A okb Aes ch sca aatE Le eR a $5 00 
Water-lantern,........ Peet Nar B a hase ssh eh cia wie gh da ainda ate a 5 00 
Bethe Cn cure creer estas aly eee Pees SAS Gis Suey emp eae exes Bf ED 
eT tee cet Pe eats ae teeing there coats ors on suets 2G o'h'g © SON 05 
Square bottle for refraction........... Sa eae oie ats Fate OMe 15 
EA IOUN VCR: FOU, ie ae rar a en le ele ai ation, acne to a haar aly « 75 
pmall double-qouvon seman spas wales a gee weng heed vs > liners 50 
Flask for condenser of solar microscope. . le 75 


Glass cylinder for experiment of the ‘ifemntaved Fete he. ea 
with plano-convex lens in place of the large flask shown in 


Mt itr cea teat mek A ol ated aie La ate ace’ alare' bv o/ dig WA xhagers 's 1 50 
een DV IGUE coi. kade ieee Ri e)s hed gyn eee cae e's #80 aie sores © a 50 
Oe, edna sos geet oases oe, fhe ee ee tae vile Wises gee hee 10 
Salcerol VeLMuiot DAE ae ea fcr ttea Uike alert incite Cewy Sdis ele Syn > 15 
Cake of emerald green paint... .......60.0ecceeees Ce At Pee 15 
Nuremberg violet, in powder, to be used with gum-water......... 15 
Two small slips of clear glass............... re aaa ads + fade 05 

$14 85 
SOUND. 

1. Heliostat, } 

2. Water-lantern, the same as under “ Light.” 

2. Plano-convex lens, . 

Peatverurn-Dall and: fie WilCow. ons Series ok ce Pere w et oiewe ees $ 05 
18. Blackburn’s double pendulum.............. ray erat tee ee 2 50 

Pe rerOL WOON aNd Oat e ak aerate 2 6 a aks o dlrab les a slue-eagpe o> 25 

ie EeigecOa fine TOMS, [OP VIDTAUGEs ois ds 0 Ales halo lene tale ae eo 25 
17. Boxes, to be half filled with sand, for supports.............. 1 00 
Eve wor pine roday Witt MiTorase. Phe eu 665 o eaie e's 28 PAN 30 
Pm ROH PTs Meet cia Pie ae tte as ates Calais dah Kats Sonne ae 75 


180 
49. “Tick for fo6tiori fork. 20 ees ae eee bt ks cate ee $ 10 
25. Wedden slide and block for fork: .2. 5.2. 3) Studs bo ee ee ee on 25 
27. Brass disk for Chladni’s figures. ...........+ wa aA eee 1 00 
S24 Tin flute &, 0, ds. Slee Se bis See cats Coa wein ce oisek 15 


33. Kundt’s experiment with whistle and tube containing silica... 30 
34, Glass tube, 3 feet long, inch in diameter................. 10 


40. .Lovers’ telephone... 2.4 smitty aoe % oes ee shellac lgawialo copes 25 
64. Two resonant bottles with glass plates...............000. 15 
47. Organ pipe-As cis 656 6. belnts 6 o's Whe Clale be ote oresete te eos) 
54. Geyer’s sensitive-flame.. .<..).52.5545.5 .c ves bens edune ee 1 00 
55. Wooden railway and seven glass marbles.............00-6-. 1 50 
57. Long brass spring-cord and resonant box.............---- 1 50 
58. Rotator, with four disks, viz., siren, Crova’s, Rood’s, and 
Maser a, (8.4545 <n eather hottest eee Hata s s te eey eee 4 50 
77. Punch for cutting holes in siren disks..............00.0.% 50 
78.. Tin, trumpetiaces st ture dg olen mee ee ee oes bald a eee 05 
81. Resonant glass tube, 1 foot long, $ inch in diameter........ 05 
100. Slinging whistle and 3 feet of large tube................06: 60 
88. -Sonometers: offen ice cree Jes coh ME a stoin a ieee en oe 2 50 
BS. ViGlinsOw yee. settee otc are eta Res oss alate solos 0 fo. 'eha es ae 50 
112. Konie’s vibrating lame? fies. disc one os bec sdea tae aed «2 60 
16. Twelve plates of glass, each 6 inches square..... ifooe pee 52) DO 
16. Bottle of varnish. ..... 20% eee euseeees e tees ihe sone need 15 
LS, Ba tes sale sees es oe Ae 8's A SUN LS oT ee Aare rie 
45, Six sheetsof-linen:paper.i.23 25 2555.5% J.uiee oe oles Sa $06 
1. 4 WX DOUNCES. 45s aot stele aces ats ole serge es cheetah an 10 
88. Rosin, 2 Ounces . 6... 2). pected ear wai qe eon ene as sels ea 10 
25. Camphor, 2 OUNCES, 6 aise 2-2 ate > ole > ainis) fev oiea tiene tae tinnes 10 
31. Lycopodium, 2 OUNCES 2. nis sss Vi osles ncele ee ss menbeam an 10 
83. Silica powder, in J-onnce bottle. 1.2... . 4-4. oi oe eee 
25. Copper-toll i. cates » oste ete wins a eine vine #nit aoe eek s Sees 05 
9/ Camel S-hdiriiercl (oe LoS ae tate tas erciye + 3 'e ctete me wee eee erie oe OS 
24 SL AD-EOLL. «2% +. ctorate Seo ee cebrle om nists ae tis ne Renee ate coe 10 
$27 50 


The numbers prefixed to the above list refer to similarly numbered 
experiments in “ Sound ” in which these articles are used. 


THE EXPERIMENTAL SCIENCE SERIES. 


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arts, and to compare the same with that of other nations. It also exhibits 
the extent to which American invention and discovery have contributed 
to the world’s progress during the last quarter century. Its production 
is deemed timely in view of the existing popular interest in the labors of 
the mechanic and inventor which has been awakened by the great Inter- 
national Expositions of the last decade, and by the wonderful discoveries 
made by American inventors during the past three years. 


The Conrrisurors whose names are given above number many of the 
most eminent American mechanical experts and engineers. Several of 
their contributions contain the results of original research and thought, 
never before published. Their efforts have in all cases tended to simplify 
the subjects treated, to avoid technicalities, and so to render all that is 
presented easily understood by the general reader as well as by the me- 
chanical student. Examples are appended to all rules, explanations to 
all tables, and in such matters as the uses of tools and management of 
machines the instructions are unusually minute and accurate. 


In semi-monthly Parts, 50 cents each. 
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PRINCE RS 


IN SCIENCE, HISTORY ann LITERATURE. 


18mo. Flexible cloth, 45 cents each. 


I.—Edited by Professors Huxtey, Roscox, and BaLrour Stewart. 


SCIENCE PRIMERS. 
Ghemistry 77.1.4 ds cee H. E. Roscozn, | Botany.........++..-. J. D. HOOKER. 
Physics.:...... BALFoUR STEWART, | LOGiIC........++-+-e0e+- W. 8. JEVONS. 
Physical Geography, A. Gzixm. | Inventional Geometry, W. G. 
Cre OlOG Vitae wk coin eee se A. GEIKIE. SPENCER. 
IPD ysiologiyaes 5-<ess M. Fostser. | Pianoforte..... FRANKLIN TAYLOR. 
Astronomy......... J. N. Lockyer. | Political Economy, W.S. JEvons, 


II.—Edited by J. R. Green, M. A., Hxaminer in the School of Modern 
History at Oxford. 


HISTORY, PRIMERS. 
GPreeCe sa. senses toes C. A. Fyrrr. | Old Greek Life...J. P. MAHAFFY. 
TROMASH Reo ees celeeie le M. CREIGHTON. | Roman Antiquities, A.8.WILKINS. 
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III.—Edited by J. R. Green, M. A. 
LITERATURE PRIMERS. 


English Grammar....R. Morris. | Shakespeare.......... E. DowDEN. 
English Literature....SToprorD | Studies in Bryant..... J. ALDEN. 
BROOKE. Greek Literature...... R. C0. JEBB. 
PHOLOGY & 25 heer eee J. PEILE. | English Grammar Exercises, 
Classical Geography..... M. F. R. Morets. 
TozER Homer...) .....W. E, GLADSTONE. 


(Others in preparation.) 


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by an agreeable, easy, and natural method of instruction. In the Science Series 
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impressed so as to retain without difficulty the facts brought under observation. 
The woodents which illustrate these primers serve the same purpose, embellish- 
ing and explaining the text at the same time. 


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APPLETONS’ SCHOOL READERS, 


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CHIEF MERITS. 


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series of school reading-books. These include good pictorial illustrations, a combi- 
nation of the word and phonic methods, careful grading, drill on the peculiar com- 
binations of letters that represent vowel-sounds, correct spelling, exercises well 
arranged for the pupil’s preparation by himself (so that he shall learn the great 
lessons of self-help, self-dependence, the habit of application), exercises that 
develop a practical command of correct forms of expression, good literary taste, 
close critical power of thought, and ability to interpret the entire meaning of the 
language of others. 


THE AUTHORS. 


_ The high rank which the authors have attained in the educational field and 
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of them have long presided, the subject of reading has received more than usual 
attention, and with results that have established for them a wide reputation for 
superior elocutionary discipline and accomplishments, Feeling the need of a 
series of reading-books harmonizing in all respects with the modes of instruc- 
tion growing out of their long tentative work, they have carefully prepared these 
volumes in the belief that the special features enumerated will commend them 
to practical teachers everywhere. 
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Wes} Ree TSO 


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Natural Selence and the Progress of Discovery, 


FROM THE TIME OF THE GREEKS TO THE 
PRESENT DAY. 


FOR SCHOOLS AND YOUNG PERSONS: 


By ARABELLA B, BUCKLEY. 
With Illustrations. 12mo. ‘ Sa: lovee ne Cloth, $2.00, 


“During many years the author acted as secretary to Sir Charles Lyell, and was 
brought in contact with many of the leading scientific men of the day, and felt very 
forcibly how many important facts and generalizations of science, which are of great 
value both in the formation of character and in giving a true estimate of life and its 
conditions, are totally unknown to the majority of otherwise well-educated persons. 
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effect its purpose.’—Huropean Mai. 


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strictly adapted to its avowed purpose of furnishing a text-book for the use of schools 
and young persons.”—London Daily News. 


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pression of admiration of the wonderful powers of the writer. And our opinion has 
increased in intensity as we have gone on, till we have come to the conclusion that it 
is a book worthy of being ranked with Whewell’s ‘History of the Inductive Sciences’ ; 
it is one which should be first placed in the hands of every one who proposes to become 
a student of natural science, and it would be well if it were adopted as a standard vol- 
ume in all our schools.”"— Popular Science Review. 


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in physical science. To the young student it is a book to open up new worlds with 
every chapter.”— Graphic. 


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